Restics output is not made to be parseable as well as it’s not primarily made to be run as a daemon like apache or sshd would be - not meaning you shouldn’t or can’t run it as a daemon with systemd, but don’t expect the output that is generated to be like apache or sshd would.
What you can do is you can use the json output to get parseable output if this is needed and then redirect the output to a file and have logrotate handle the rest.
Restic is designed to run on many different OSes in a variety of configurations. For example, restic does not need to be run as root/Administrator.
Considering this, it would be infeasible to come up with a set of rules that provide centralized logging. Where should user instances log vs. root instances?
It’s much simpler to let the system operator configure this by redirecting output. Or, for example, if the script is run from cron then cron will email any output to the local user who runs restic from their crontab.
The answer for others looking for info about backups, a brief overview of results can be logged by adding > /foo/bar/restic.log to the backup command which produces exactly what I was after