Thank you, Jon, and Happy 2020!

I manually created the account for Public, which worked instantly.
It also propagates any updates to the server, which does not seem to work for me with the Assistant setup.

However, it has the same limitation as the Assistant setup, which is that subfolders of Contacts are ignored. I tried to append the subfolder name to the server path, but this seems to have no effect.

Second problem:
When setting up the second account for the personal contacts, OS X gets stuck with "the account is already existing", querying the password again and again. I tried using user(domain.com) instead of user<_at_>domain.com (as suggested by GFI) for one of them, but it does not seem to avoid that error.

Cheers,
Philipp