ConfigurationDirectory 'matrix-synapse' already exists but the mode is different. (File system: 700 ConfigurationDirectoryMode: 755)

After restarting Synapse I get the above in the output of systemctl status.

I think that the mode should be 700 or 750 (with the group of the directory set
to a matrix-synapse group not nogroup).  It shouldn't default to world
readable, and it shouldn't whinge when the directory isn't world readable.

Also files with secret data such as homeserver.yaml and homeserver.signing.key
shouldn't be world readable, they should be 600 or 640.

https://wiki.debian.org/SystemGroups

The above Wiki says:
nogroup (user: nobody): Daemons that need not own any files run as user nobody
and group nogroup. Thus, no files on a system should be owned by this user or
group.

Files with secret cryptographic data definitely shouldn't be owned by nogroup!