Surfacing the logs to a syslog server or the like

[psyciknz]

After having an issue (reported by backblaze where my backup wasn't running), I started looking for the backblaze client logs. Found them under various subdirectories of

/config/wine/drive_c/ProgramData/Backblaze/bzdata/bzlogs

But now I'm wanting to push them to a sys log server. It doesn't look like rsyslog is part of the container, so I might be up for a custom build, but has anyone tried similar?

Or even just getting the backblaze logs into the docker logging?