For those people to lose in addition what is, for many of them, their only connection to the wider world just makes it worse.
For those people to lose what is their only connection to the wider world just makes it worse.
The simplified version is missing two prepositional phrases: "in addition" and "for many of them". Those phrases don't participate in the grammatical relationships between the rest of the constituents. Yes, you should be able to parse the sentence without them, and use that to help you understand how to parse the sentence with them.
... to lose what is their only connection to the wider world ...
... to lose {something}
The structure "what is their only connection to the wider world" is variously called a content clause or a fused relative clause. It might even be called an embedded question. It acts as the direct object of the infinitive "to lose". The fused relative label indicates that the function of the single word "what" is the same as both a demonstrative "that" and a relative "which":
... to lose that which is their only connection to the wider world ...
and this can also be paraphrased as
... to lose whatever it is that is their only connection to the wider world ...
In short, the original is a simpler structure.
what is their only connection to the wider world
The "what" is the subject, the "is" is the verb, and the rest is the subject complement. Rather than thinking of it as a question, we can think of it as the question's answer. In the original context, it represents something like "mobile networks".
For those people to lose {mobile networks} just makes it worse.
... what is, for many of them, their only connection to the wider world ...
Not everyone who is stuck at home relies on mobile networks, but many of them do.
We can't simply insert an "it" before the "is", or even change "what" to "whatever it". If we do that, then "their only connection to the wider world" has no way to connect back to the rest of the sentence. The phrasing "what it is" has a subject, verb and complement. "What is" has only subject and verb, allowing "their only connection to the wider world" to act as compliment.
