Shortly after merging an older catalog into the current (all ready very large) catalog, we started having this problem. The merge completed successfully and Lightroom did a "compression" (?).
Now, after doing multiple edits (hours), when shutting down, Lightroom frequently has a problem doing the backup. "Lightroom encountered a problem when reading a catalog file"
Restart and "Lightrom must now check the catalog before proceeding". Completes without error. Shutting down now, the backup is successful.
Plenty of space available on the drive holding the catalog and backups (two different devices).
Sorry that you're facing problems backing up your catalog as you're getting an error message which reads: "Lightroom encountered a problem when reading a catalog file"
Where is your current and larger catalog saved and what size it is currently? If on an external drive/flash drive, please make sure there are no connection issues(rare but possible, however if the older catalog was located somewhere else then it could be related). So basic things you can try:
If there's no go with the above steps, I'd recommend that you restore Lightroom preferences to default, here's the linked content for details on how to restore preferences: How to set Lightroom Classic CC preferences
Let us know how it goes.