Walls were not prepped properly, cleaned, etc. New paint is sitting on top of slime/grime and conversely comes off easily as it is not adhered to the wall. Just my thoughts.

I dont know about dirt and grime, but, there was most likely soap scum that wasnt cleaned off. Also paint isnt the best thing to have on a shower wall in the first place. It should be a shower insert, or tile, etc.

There is tile but wall in upper part

main concern is did they paint over wall that has mold

Besides possibly not cleaning prepping properly before painting maybe old paint was oil based and now repainted with water base paint again without proper preparation. The slimy feeling after a shower is probably just condensation. I wouldn't be worried about mold unless you see it . Personally myself I open window prior to showering.