I sometimes see that. I have not tried to investigate. It doesn’t happen on every boot. So I don’t worry about it, on the assumption that it won’t hurt too much if log rotation is delayed.
And also getting Failed unmounting /var at shutdown.
That could be more serious. Or maybe not. Hard to tell.
I don’t have a separate “/var” so I am not seeing that issue.
If I did see that happen, I would boot from rescue media, and run “fsck” on that file system. If it shows the file system as clean, then it was probably unmounted later during the shutdown. There’s a final “unmount all file systems” check near the end of shutdown which usually catches ones that failed earler in the shutdown.