The Debian installation has never seen anything from Bitnami before because it was installed just a few days ago.
Thank you for the hint with the Bitrock installer logfile, here it is: bitrock_installer_599.zip (3.4 KB)
In line 327 I can see an error. I can imagine that my first name (which I gave the Bitnami installer to create the administrator account) is responsible for this because it contains a non-ASCII character - my first name is "André". I will now reinstall Bitnami Redmine only using ASCII characters for my name, and report back.
Edit from a few minutes later:
It was indeed my non-ASCII first name. Now when only using ASCII letters, there weren't any problems.
Please let me suggest an additional check for the installer so that it warns the user when a database task fails, like it was in my case. Or you just check the user's input for non-ASCII letters.