MacOS – Does Time Machine Copy Renamed Files

Some experimentation using the xattr command shows this:

• Label information is stored in the com.apple.FinderInfo extended attribute, which every file should have by default.
• Custom application associations are stored in the com.apple.ResourceFork attribute, which not every file has.
• Updating the FinderInfo attribute does not cause the modification date to be modified.
• Creating/updating the ResourceFork causes the modification date to be modified.

The resource fork historically had a special place in Mac file systems. I'm not sure if the com.apple.ResourceFork extended attribute is the same as a resource fork, if the latter was superseded by the former or how else they are connected.

If there's a technical difference between an extended attribute and a resource fork, it may be "necessary" for a file to be modified when the resource fork is updated, but not when the extended attribute is written.
It may be that the (legacy) API for updating resource forks updates the file modification date in the process, while the extended attribute API doesn't. The latter possibly in error, possibly because of different philosophies.

Vague information, but it might give a little more insight. In the end though you're right. Some meta information modification causes the modification date to be updated, others doesn't. Whether there's a reason behind this or if it's just an oversight… only a few guys at Apple may know. :)

I believe this is a staleness prevention. That whenever there is too long between backups Time Machine uses a more thorough way to ensure that the backup is complete.

It is my understanding that the 40 GB is a "this is how much we consider for backing up" and that the actual data transferred may prove to be a lot less if the files turned out to still be identical.

Based on your description I believe that you have reached a point where you need to let your Time Machine backup catch up - work on its own until it is done, if at all possible. If you cannot wait for that, perhaps now is a good time to buy a new drive and use that instead and have the old drive as a backup backup.