We got a slightly similar experience with @Hetzner_Online@social.cologne in 2021, following a bogus claim by a copyright troll ("DMCA Force", seemingly working for the game development studio Cyan Worlds).

At no time did Hetzner try to check if the claim was legit, and forced us to take down all of our websites (at least they did not deleted them with no prior warning). They immediately sided with the copyright troll, against their legit paying customer.

We managed to get an apology from Cyan Worlds, who promised they are going to be more careful in the future with who they work with, and made the copyright troll retract their claims. But nothing from Hetzner. Not even an informal apology. Not even an acknowledgement of the claims retraction.

In our case we moved to self-hosting to ensure this would never happen again, but this might not be a good solution for you if you have much bigger hosting needs.