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I. "Modular" (furniture) IKEA, also in UK

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Ref. IKEA modular kitchen:

Ref.Alibaba.com

I. "Modular" (furniture) IKEA, also in UK

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Edit 1.
I find assembleable and disassemblable (suggested by OP but not listed in my Oxford Advanced Learner's dictionary)not easily pronunciable as other commonly used terms like

• Modular furniture
• Flat-pack furniture
• Self-assembly furniture
• Knock-down furniture
• Detachable furniture (term used in other countries)

Ref. IKEA modular kitchen:

Ref.Alibaba.com

I. Detachable= can be disassembled and assembled.

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Ref. IKEA modular kitchen:

Ref.Alibaba.com

I. "Modular" (furniture) IKEA, also in UK

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Ref. IKEA modular kitchen:

Ref.Alibaba.com

I. Detachable= can be disassembled and assembled.

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Ref. Alamy Detachable Laptop:

,Ref.Alibaba.com

I. Detachable= can be disassembled and assembled.

OP's query

The context is like: “This table from IKEA comes in parts and thus ‘assembly-able’” Meaning it can be assembled and disassembled. .

"Modular" is the adjective used by IKEA, for furniture and kitchen, that can be assembled and disassembled. This term is also used in UK as per the website:

Ref. Designer kitchens for less - U.K.

What are modular kitchens?
Modular kitchens are kitchens that can be assembled using individual units, these units are then fitted to form the skeleton of your new kitchen. https://www.designerkitchensforless.co.uk/blog/the-guide-to-modular-kitchens/#:~:text=What%20are%20modular%20kitchens%3F,up%20with%20the%20doors%20fitted.

Another word is detachable. which is used by Alibaba and some other sites. Though "Detachable" is commonly used meaning partly removable components. It is also a term used for complete assembly and disassembly.

II. "detachable" and "modular" meaning..
Ref. Collins dictionary.

detachable..
adjective.
If a part of an object is detachable, it has been made so that it can be removed from the object.
...a cake tin with a detachable base. Examples :
The clear lenses are detachable and the frames washable.
The Guardian (2017).
. There's a car with a detachable motorcycle stored inside it.
The Guardian (2018).
.
2.modular.
adjective.
consisting of separate parts that, when combined, form a complete whole: modular furniture.
Modular classrooms were built to remedy the problem of overcrowding in schools.
Modular shelving can be configured for anything from a desktop computer to a whole data centre.
The modular design allows for the building to eventually accommodate 600 students.

III. Detachable is a versatile adjective.

In general, "detachable" is a versatile adjective that can be applied to various contexts where parts or components can be separated or disconnected, including:
-Furniture (legs, shelves, etc.).
-Mechanical systems (hoses, pipes, etc.).
-Electrical systems (connectors, cables, etc.).
-Industrial equipment (modules, components, etc.)

Ref. IKEA modular kitchen:

Ref.Alibaba.com