There is probably not a clear answer. If you want to be on the save site cut off an inch or two (maybe more) of the drywall with the saw and use concrete expansion foam (comes in rolls) where the drywall was (glue it on). The kicker board will cover later everything.
I probably would fill the low areas to prevent trip hazards but also probably would not put anything down other than indoor/outdoor carpet a power outage or another pump failure and then any new material other than designed for wet dry will hold more water even with a proper slope . So yes fill the low spots , but reconsider any type of structure that ...
How old is the house?
This sounds like an old house given a 1-2" deep puddle and painted concrete.
You should consider that :
- the slab is probably too thin
- inadequate drain rock under the slab
- no insulation under slab
- lack of radon / vapor barrier under slab
- the exterior perimeter drain may be clogged
- sewer service pipes in slab may be ...