Hi,
Good,
Each user + the system has his own dbus. Normally, you should have dbus.service and dbus.socket units somewhere (/usr/lib/systemd/user and/or /etc/systemd/user and/or .config/systemd/user)
If it works correctly for one of the users, then probably /usr/lib/systemd/user and /etc/systemd/user are fine, and there is an override which breaks the things in .config/systemd/user/dbus.*
Thanks again for the hints. For both users there are only the backup.service and backup.timer in .config/systemd/user, no dbus.*
Note: If the non-working user is an "old" one, it may be explained by the fact that those unit files are quite "recent", so probably there is an history there.
The working user is older than the non-working user. I took a look into /etc/systemd/user/sockets.target.wants, dbus.socket is not enabled there. Regards Bjoern