Get Time Machine to fully recognize past database
Background: A problem corrupted the file system on my directly-connected Time Machine disk so that it became read-only. After many weeks of torture (permissions errors and kernel panics), I have the backup database copied to a non-broken disk. (Copied with Finder's "Paste Items Exactly," so metadata should be preserved.)
Command line tmutil was needed, but Time Machine now recognizes the repaired/new disk, and I can use the "Star Wars" interface to browse backed up files. However, in Time Machine Preferences, "Oldest backup" and "Latest backup" both say "None." So I guess Time Machine doesn't completely recognize the repaired/new disk.
I've not yet run a backup since the repaired disk was attached. How can the old backup be fully re-connected to Time Machine?
iMac 21.5″, macOS 10.15