Lowe’s and Home Depot sell a product used for shower wall. The pattern looks about the same as your surface pattern. You could put it up with double backed tape. Of course you’d have to push the wires up in the hole.
Any idea what this was used for?
Personally I would try cleaning,the mess up with something like Awsome cleaner possibly lightly using a scotch rite pad. Once clean put a SS screw in the screw holes. Maybe use a bit of Dicor or some other white caulk to fill the big holes. You should be able to match the texture pretty well with a little practice and patience. Worst case paint the ceiling using a off white paint