So what happens if there is a law which prescribes this but the law is deemed unconstitutional / incompatible with EU law or something like that? Specifically in the case where it is in use for a non-zero amount of time before being removed again?

To be honest, I don't understand YES betters. Each second asylum seeker threw away their documents according to a report a few years ago: https://www.welt.de/politik/deutschland/article226900563/Jeder-zweite-Asylsuchende-kommt-ohne-Papiere-nach-Deutschland.html

Jeder zweite Asylsuchende kommt ohne Papiere nach Deutschland - WELT

Wer in Deutschland Asyl beantragt, kann seinen Namen, Geburtsdatum und seine Nationalität oft nicht nachweisen. Jeder zweite Asylbewerber reist ohne Pass ein. Und das auch, weil es die Chancen zu bleiben erhöht.

(OK, a small minority might have lost them).

Do people think that this will change or that Germany won't take (non-Ukrainian) asylum seekers anymore?

The probably only possible coalition partner (SPD) that the CDU wants says that they won't cooperate: https://www.tagesschau.de/inland/bundestagswahl/klingbeil-spd-union-migration-100.html

My prediction: The left always wins in Germany and Merz will drop his hardline stance after the election.

I am really curious about this one, because it is hard to imagine this from the center left government we will be getting, but not doing it Merz would instantly violate his promises.