Several people here have tried to bring clarity to the OP’s problem.
Can I try to clarify things further?
We know we’re dealing with the metal tab variety of female threads.
We don’t know whether they are M3.5 or 4BA.
We know an M3.5 screw won’t go in but we don’t know whether this is because it is an M3.5 female thread and it is damaged or because it is a 4BA thread, which may itself be damaged.
Recutting a 4BA thread to M3.5 isn’t really doable, for reasons DC31K tried to point out. Hence, if it is 4BA, advising you to get an M3.5 rethreading driver isn’t very helpful advice. Even if it is M3.5 all along there is no guarantee, in my experience, that a very short, already compromised M3.5 thread in back boxes or pattresses can be made good again with just an M3.5 rethreading tool. Same applies to 4BA, i.e. if the thread is 4BA you have chance of rethreading it with a 4BA tap, but it may be too reamed out and messed with for this.
This is really why I suggested the T nut repair earlier. You can easily make one yourself in 4BA (or M3.5 if you had a tap) and end up with a secure fix that won’t need revisiting. Bear in mind that when plugs are removed from sockets the face plates can be subjected to quite a strong pull and any weakness in the tiddly faceplate fasteners is likely to be found out sooner or later.