As it turns out, my tag editors were both set to preserve the modified date of files when tags were edited and saved. So I turned the setting off and repeated my previous experiment. This time, ‘Refresh Metadata’ did not pick up the change, but ‘Scan Library Files’ did.
It will take some more testing to determine if this will be the case for all tags. But if that is the root of all the Plex Dance issues, we should have had this conversation 3 years ago.
The fact that tag editors can be configured to preserve the Modified timestamp is still a challenge.