This flat is messy/untidy.
I want to say the flat is rather disorderly, not perfectly neat, chaotic, with things all over the place, with things being (possibly purposefully) badly arranged. I don't want to mean it's a dirty/filthy place.
I am wondering whether it's a proper word choice and whether I would need to elaborate further to reduce ambiguity. Dictionaries mention 'dirty' being a synonym for both words.
No, neither messy nor untidy necessarily imply dirty. Something being messy or untidy means that it's disorganized, or chaotic. For example, as you pointed out, a room could be messy, but spotlessly clean.
In general, when something is messy, or untidy, there's a decent chance that it's also dirty, but that is not guaranteed. If you want to be explicit about it, to avoid offending someone, say, that's fine as well, but not strictly necessary.
Conversely, something could be dirty, but very tidy. For example, a room that was well organized but has been abandoned for a long time, might have accumulated a layer of dust on everything. In that case, you would describe the room as tidy, even though it's dirty.
The best choice for your purposes would be untidy. This would cover the situation where things are all out of place but they could be perfectly clean. Messy is slightly ambiguous as it covers both untidiness and dirtiness and so might give the wrong impression.
In a comment RonJohn suggested that there is an imperfect US ordering: untidy, messy, dirty, filthy. That works too in the UK too.
I would say "cluttered". It basically means the same thing as "messy" or "untidy", but the connotations are different.
If your apartment is cluttered, it could be due to your flighty or eccentric personality. You probably move from task to task, maybe never finishing one and putting the stuff away first.
In describing the apartment, you could elaborate and say "the apartment was cluttered with the tools of countless tasks in progress", or similarly, "cluttered with mementos and keepsakes attesting to a life well lived", or "cluttered with trophies from her athletic career", etc.
If your apartment is messy, it's probably because you are too lazy to clean.
I would not say "chaotic", because chaos is a dynamic state. "clutter" + "tornado" = "chaos".
I'd like to point out that tidy with respect to having things in order is a nearly exclusively British word. We Americans use untidy (although not often) in the sense of messy, but the Keep Britain Tidy signs around the UK roads are Keep America Clean signs in the US. Americans will say clean and tidy to add emphasis to the word "clean," but very rarely use "tidy" on its own in this way. Of course, since you are saying "flat" instead of "apartment," it would seem that you are looking for British English, but I thought it might be useful to mention this.
I believe I understand what you are looking for. My father, a law professor and writer, had in his office a folding banquet table of the sort that would seat 12, always covered entirely with at least a hundred books. Some would be opened to a particular place and placed on their faces in lieu of a bookmark, with others similarly opened and stacked on top of them. You are looking for a word to describe this sort of situation.
A French friend of mine once referred to her children's playroom with the wonderful le bazaar, but we don't have anything that captures the idea quite so colorfully. Disorganized is a neutral word, simply meaning not organized. If you want to avoid the idea of dirty, you could use, to add a few to the suggestions already given, haphazard, disorderly, or the understated unsystematic. The latter can convey a rather humorous attempt to be polite: "'The flat was organized in a way that might be described as ... unsystematic,' he said, sardonically raising an eyebrow."
In this context, I would absolutely use a word you’ve already used: chaotic! Untidy could convey something as simple as a bed being unmade, and messy could mean anything from toys scattered on the floor to plates of half-eaten food laying about.
‘Chaotic’ would just convey a great deal of objects and strange arrangements, and importantly, unlike messy or untidy, it doesn’t have a (necessarily) strong negative connotation.
The answer to the actual question in the title is simply "No."
The OP mentions having found a synonym in a dictionary, ignore that reference.††
"I am wondering whether I would need to elaborate further to reduce ambiguity."
This is a great question. The answer is simply:
Yes.
English is incredibly ambiguous, everywhere, always, universally and ubiquitously.†
A very common phrase here is "clean but untidy". (Or variations such as "disorganized by spotless" and so on.) For exactly the reasons you have identified, as I say the phrase "clean but untidy" (and similar variations) are commonplace.
† An interesting point is that on this site: There are literally 1000s of questions from English learners which say: "I am shocked, shocked, shocked, shocked, shocked, shocked, shocked, shocked, shocked, to see that this sentence _ _ _ _ is ambiguous. So far, 490 English native speakers have told me to my face that (A) it is normal that sentences in English are highly ambiguous and that (B) the particular sentence in question is ambiguous. Obviously all 490 people are totally incorrect. Tell the exact correct version of the sentence that is not ambiguous. Tell me now!" You can probably seem my humorous sarcasm here. Pointing out something in English that is ambiguous is like calling a news conference to announce that you noticed the sun is hot. Ambiguity in English is a non-issue. English is ubiquitously ambiguous.
†† You may be wondering why to ignore that reference. The reason is that synonym is ................ extremely ambiguous in English. Ignore the reference.
