Is that tile? Kind of hard to tell from the picture but looks like a couple of lays of joint compound or a skim coat of plaster.

If you just plan on reinstalling the sink, couple or three coats of joint compound. Smooth it out and paint.

The paint bubbling around the drain line might be something you want to take a look at. Usually that’s a symptom of moisture.

I would use Durabond drywall compound rather than premixed joint compound. Durabond is a setting type compound; it's the stuff sold in bags that you add water & mix. Durabond is stronger, sets up faster, less shrinkage & tendency to crack. Known as 'hot mud'; comes in various set-times. If you're a novice, get one w/ a longer set-time. Like Durabond 45 (45 minutes set time.)

But, before you even think of what is going to coat the wall behind the sink, make sure that you have a strong substrate behind the plaster to bolt the sink to. If you are putting it back in the exact smae space, are the holes where the old bolts went going to hold the new bolts now that they have been pulled out? Maybe not. You may want to cut out a section of the wall back to the studs and replace it with a 2 x 6 firmly screwed between the studs. Then put on the finish coats. You can screw right into that and be as solid as you need to be.