This actually turned out to be a postfix issue, as @youhost already initially suspected.
So the mail container would not start, since postfix was running and hogging port 25. The solution in this case is to stop and disable postfix:
root@my:~# docker restart mail
Error response from daemon: Cannot restart container mail: driver failed programming external connectivity on endpoint mail (80745a182e99c96ca09dcb0a3775c919d7cd6907ba060410d860b2bd5929440e): Error starting userland proxy: listen tcp4 0.0.0.0:25: bind: address already in use
root@my:~# systemctl status postfix
ā postfix.service - Postfix Mail Transport Agent
Loaded: loaded (/lib/systemd/system/postfix.service; enabled; vendor preset: enabled)
Active: active (exited) since Sun 2021-08-29 20:16:02 CEST; 2 days ago
Main PID: 1654 (code=exited, status=0/SUCCESS)
Tasks: 0 (limit: 4653)
CGroup: /system.slice/postfix.service
Warning: Journal has been rotated since unit was started. Log output is incomplete or unavailable.
root@my:~# systemctl stop postfix && systemctl disable postfix
Synchronizing state of postfix.service with SysV service script with /lib/systemd/systemd-sysv-install.
Executing: /lib/systemd/systemd-sysv-install disable postfix
root@my:~# docker restart mail
mail
root@my:~#