My Time Machine is backing up in /private/var/folders/ My MacBook Pro (10.15.7) is backing up parts of the drive I didn't expect. I have been cleaning up and excluding directories, but this time I found something I thought was excluded by default:
private/var/folders.
To examine I have been using 'Timedog'. Here is a piece of today's output:

Again, as far as I know and as referenced here, the standard exclusions
/System/Library/CoreServices/backupd.bundle/Contents/Resources/StdExclusions.plist

include ('exclude') private/var/folders/ under the &quot;contents excluded&quot; category, meaning that the folder container is backed up but nothing inside. Clearly here we have 42.6 MiB of content.
This is an attempt at a (partial) answer. It is too long for a comment.
Apple makes changes (mostly minor) to Time Machine without notification or  documentation. I believe that the question and answers here are too old to be reliable for recent versions of macOS.
The StdExclusions.plist does not exist inside the backupd.bundle on macOS 11, so that is no longer a mechanism for exclusion.  I don't know if it exists in macOS 10.15.7. And even if it does exist, whether it is used.
Mike Bombich of Carbon Copy Cloner specifies what is excluded by CCC and says that it excludes only part of /private/var/folders.  He lists these as being excluded:

/private/var/folders/*/*/C
/private/var/folders/*/*/T

Of course, that doesn't directly imply that Time Machine is doing the same, but it is a pointer.
On my Mac some files are from /private/var/folders are included in Time Machine.  My Time Machine snapshots include just these:

/private/var/folders/*/*/0/...

This is all largely circumstantial regarding Time Machine, but does suggest that the exclusion mechanism is more complex (or should I say hidden) than most of us expect.
Just to muddy the waters, I have to admit that the exclusions.plist file included in the root of every Time Machine (macOS 11.2) snapshot does list /private/var/folders as being excluded!
Finally, my advice is never to attempt a cleanup of system exclusions if there is any likelihood of wanting to do a full restore.