Why does 'df' not show changes after running CleanMyMac?
Taking @at0mic's comment as a starting point, I have a theory about what's happening:


Since the Time Machine snapshots aren't physical copies, they're still hanging on to the same inodes that CleanMyMac deleted.


Since the snapshots didn't take up more room when they were created (see https://www.zdnet.com/article/the-apple-file-systems-killer-feature-clones-and-snapshots/ - they just create one more reference to the same inodes), I also won't get back disk space right away when deleting stuff.

This makes sense to me.  However, when I went into Time Machine and performed "Delete all backups" on one of the large items I'd deleted, the disk usage as reported by df still didn't reduce.  So I kind of believe that Time Machine is the explanation, but there are still pieces I don't understand, so if I figure it out I'll edit this answer.