Time Machine tries to back up /Volumes/.timemachine

Today, I attempted to restore a file from the Time Machine backups stored on my ReadyNAS and, at first, could not get the Restore button to show active (instead of gray).  After reviewing Time Machine log files, I saw that Time Machine was trying to back up (or at least access) one of the volumes mounted from the ReadyNAS even though that volume shows in the Time Machine exclusions list.  After unmounting all volumes shown as mounted from the ReadyNAS I went back to the Time Machine restore browser and found it more responsive and was able to restore files.

I reviewed logs again and found there is still an error in the logs which I think I could get rid of if I excluded the /Volumes/.timemachine volume from backups.  The error is,

    Failed to create volume info from disk '<TMDisk: redacted_hex_number>  '/Volumes/.timemachine/RNAS._smb._tcp.local./REDACTED-UUID/timemachine'', error: missingName

I believe the usual way to exclude a mounted volume from Time Machine is to drag it from a finder window into the exclude configuration window for Time Machine.  However, this particular volume does not show in the finder network volumes list, perhaps because it starts with a period character or is in some other way hidden.

The command line utility called tmutil has an option for excluding a volume but I am reluctant to mess too much without knowing exactly what is going on.

Why is Time Machine emitting that missingName error?

On a related note, some earlier performance problems may have been caused by having less that 20% free space on the NAS.  (I freed more than 20% before the problems described here occurred.). I kind of remember that when the free space gets below 20% Time Machine performance can get so bad that backups fail.

I have 12TB of storage.  Is it really true that more than 2TB of my disk space has to be empty for the NAS to have reasonable performance?  How does it use that "empty" space?

MacOS: Ventura 13.4.1

ReadyNAS firmware 6.10.8