get it skimmed! Don’t bother with the dry wall filling nonsense, that’s for commercial buildings, offices and the like. Anyone doing that domestically is either a cowboy or a proper tight arse! You just won’t get a quality finish.
Then paint the skim, but DON’T pva it first ffs! Thin some cheap white emulsion 50/50 with water, make sure its not vinyl or silk though. Give it 2 coats of that, then put 1-2 coats of your colour etc. In a warm room, you might be able to do the whole job in a day if your colours are light. If dark, wait 24hrs.
Make sure the plaster is dry in all areas before you paint, give it 2-5 days depending on thickness.
PVA will not bond skim & paint properly and eventually will peel off, probably next time you come to paint. Meaning you will most likely have to skim again to get a perfect finish