External trade, damage repair, warranty?

Then just tell him 2k or get out. He will manage that.

Have you confronted him with this question yet? Does he feel like tearing everything out again and re-tiling it EXACTLY? Also tell him that all the sanitary installations must be professionally re-installed. You can tell him that a precise inspection will be done beforehand with an expert, and afterwards it has to be exactly the same again. Scare him a little, list all the small details that would add up. Then he can already sum up in his mind all the working hours, the materials, the effort. And then say that you would agree to a 2,000 euro discount and that he never has to see you again.

Yes, he is aware of all this, his offer would be that we still pay the 500.-€ (we had withheld 2000.-€ from the final invoice) and leave it as it is or he does everything new.

Another question - is the deviation definitely a defect? (I have no knowledge about this at all)
That means you have the right to demand rectification? (Background: To me, it sounds like he doesn't even expect to have to redo everything)

This is a very difficult decision. And, - sorry! - I am really relieved that I don’t have to decide something like this! Maybe bluff and say that he should redo it, set a fixed deadline, and then hope that he still agrees. I also wouldn’t agree to pay the 500 euros.

Do you have nothing in writing about the agreement to deduct 2,000 euros? Or witnesses?

But we have it in writing, but with the addition that the final amount is yet to be agreed upon.

Invite him and watch the fiasco together. Start listing the work steps and casually ask when he would be finished. The start of the work, of course, should be immediate. If he then looks dumb or starts saying "I thought we'd settle this through the retention," you know what he prefers - additional work or writing off money. If the latter, you say "I thought you wanted to do it completely new, 2000€ was too much for you. I would agree with 2000€ and the matter is immediately settled."