Looks like that is a retrofit junction box, so it should be a fairly easy job for an electrician, to put in a new one, and get it all hooked back up for you. Its not a big job, but, anything electrical, can be a expensive. However, its better to have an electrician do this, so it is mounted properly. It sounds like it probably wasnt, since it should not have come down that easily.

If larger screws don't work, replace the box please.

You could try stratening out the tabs if bent and re tapping the screw holes. If #6 tap to #8 and if #8 tap for a #10.

Turn off power and push wires to the side not being worked on.

If this sounds like too much, call an electrican. retapping or swapping the j box wont be hard.

What Dave said is a good idea. Or, epoxy 6-32 studs (cut some screws off) into the old holes and use nuts to hold the adapter plate in place.

Thank you so much ! Previous installer definitely put in short screws that were barely reaching the wall, let alone the junction box.
I tried the longer + larger screws & it worked ! This is just temporary until I can get an electrician to come out to update.
Thanks so much for all of the helpful information, your responses helped me realize I should call an electrician for my first encounter with wiring : )