As I just can’t figure out what was going on, I’ve made a fresh Ubuntu VM and installed everything from scratch. Now everything is working correctly, including the nightly backups. Where I think I went wrong with the first installation is that:
(1) I ignored the section to create a dedicated bitwarden user. It was optional, and because the VM is dedicated to bitwarden, I figured it would not add any security so I skipped it. But I therefore also skipped the steps to create the /opt/bitwarden directory, and installed it into my home directory instead. One of the error messages from bitwarden-mssql was that it couldn’t find certain files below /opt/bitwarden/bwdata, which should have been /home/myusername/bwdata in my old installation. I guess those must have been hard-coded? So following the creation of the bitwarden user + dedicated folders must have solved it.
(2) As I was required to sudo many times, I just did sudo su and went on with installation, changing configurations and adding scripts for self-maintenance. This I think probably messed with ownership on certain containers, files etc.