Time Machine Can't See Old Backups

[describemushroom5011]

Time Machine can no longer see my old backups.

I have a Macbook Pro 2017 running macOS Catalina 10.15.7

I have a Time Machine backup on an external hard drive formatted as a HFS+ / Mac OS Extended with dozens of backups going back to 2019.

When I entered Time Machine to look for an old version of a file, I noticed that I could only see the last 3 backups on the sidebar.

If I go to the actual folder inside my Time Machine volume's /Backups.backupdb/ folder, I can see dozens of backups going back to 2019.

When I go to my Time Machine Preferences, the oldest back up it can find is only from 2 weeks ago.

The older backups seem to be no longer readable or visible to Time Machine.

Something odd I noticed is that for the backups that are visible to Time Machine, the folder structures look like this:


There's 3 folders, Macintosh HD, Macintosh HD 1 and Recovery. Inside Macintosh HD is a single System folder, and inside Macintosh HD 1 is where the actual backup of my hard disk is.

If I look at the backups before then which Time Machine can no longer see, it looks like this:


It only has a Macintosh HD — Data folder. It seems to me like something changed in terms of how Time Machine does backups between the working backups and broken backups.

I've already tried running

tmutil associatedisk -a /

and

tmutil inheritbackup

based on old Pondini troubleshooting pages (E2 and B6), and it hasn't fixed it.

I haven't ugpraded OS or changed the setup of my Time Machine backup recently either (i.e. changed locations).