Poor painting work or poorly plastered?

It’s not about a defect. I just want to find out what happened and then have it fixed at my own expense. I suspect that it was not re-plastered and sanded. Now I wonder, can the painter still catch up on that?

If it’s not about a defect, why does the title say “Poor work by…”? What happened? You ordered and received Q2. You wanted a coat of paint and got it. Improve? So it’s poor work after all… Re-plaster and sand? That’s not necessarily required with Q2. If you don’t like the result now, you’ll just have to spend T€ 10 and have the whole house completely redone. The painter will surely be happy to do that.

Improve? So it's bad work after all...

One can also want to have correct work improved if one is not satisfied with the result.

Yes, it works. So at least any reasonable painter should still be able to manage that now. Unless he knows that his paint is really bad and that he can't (or doesn't want to) sand it down and nothing else will stick to it. But yeah, for a grand he won’t do it even without bad paint.

The plaster is Q2 and the painter simply painted over it.

I have problems with the evaluation of the plaster because the quality of the photos is not the best. They are mobile phone photos, and the phone software does quite a bit itself.
What I see has little in common with our own Q2 plaster. Even Q2 is fine-grained! What I see here is more like our exterior plaster structure, which is coarser.
Additionally, it looks like the painter used too little paint.

As I said before: what you see in the photos may possibly not correspond to reality.

If you are already willing to pay for the rework anyway and it is not about warranty or similar, I would probably just openly discuss it once with the painter. What else can be done, what do you actually imagine, and how can that be achieved best. Or something like that

Q2 is also fine-grained! I see our exterior plaster texture here, which is coarser.

Exactly! What kind of plaster did the plasterer use? That looks like roughcast. Furthermore, I see the "mistake" with the painter here. Even as a "professional," he has some duty to inform the layperson that you should not just paint over such a surface. But who knows what kind of "professional" was at work there. The OP can surely say more about it—if he wants to.