The shower drain was installed incorrectly - tolerate it or not?

Depends on the price/the reimbursement. I wouldn't care, but I also hang posters crooked

Is it normal that the gutter is directly adjacent to the wall at the back? I only know it with about 5 cm distance to the back...

It would probably be too risky for me that after moving, nothing is sealed anymore, that the underfloor heating might be damaged when breaking out the screed if necessary, or some other technical problem arises. Yes, it looks sh***. But leaks would be even worse. Apart from that, does a company have to make repairs even in a "disproportionate" manner? It's "only" an aesthetic defect, which alone causes a few hundred euros in costs just by removing/reinstalling the tiles. Then probably work on the screed, bending the pipes... I can't imagine that one would win legally there...?

Someone once wrote that in the case of a purely cosmetic defect (depending on the severity), one is only entitled to X% of the correction effort. In other words, the craftsman is not obligated to correct it at his own expense. That makes some sense, I think... even if it is annoying for the client.

I find it strange that the gutter connects directly to the wall; I am not used to that either. I don't know if that has negative consequences.

The risk of botching the correction is definitely high. However, it would also annoy me enormously to have to look at it every day. Therefore, try to negotiate the highest possible compensation. This just seems to have turned out rather unfortunate. That the tiler didn't notice this while laying the tiles is absolutely incomprehensible to me.

I am actually more of a picky type and I really like things straightforward and accurate. But this visual defect in the shower would actually not really bother me, I have to say. It is still annoying, no question.