Hmm, OK. I actually stopped the "Cleaning up old backups" after 36 hours last night, because my computer had slowed to a crawl for everything else and apps were crashing - so I pressed the X in Time Machine and, after that stopped, restarted the computer. I then restarted Time Machine with my second Time Machine external HD (and a more reliable drive, for that matter).
As of now, it's been "Cleaning up all backups" for 12 hours; I tried the "tmutil listlocalsnapshotdates", and got just five dates, going back only to 2022-01-21. I don't know if that means it's cleaned up to that most recent date or not. (If so, wow, this backup is losing a lot of the "time machine" part of this!: on the Time Machine drive itself, the oldest folder is 2021-03-25)
If Time Machine is just doing its thing and taking 12-36-48 hours is normal, then I'm fine letting it run its course; what I wish I were better able to determine is if something's not working and I should intervene.
For what it's worth I only use Time Machine with hard drives directly plugged into my computer. One stays always at my desk; there are another two that rotate between my computer, and my office at work, so there's a backup at a different location as well.
Side point: there is almost no "new" material in these backups - it's just lots of media moved to a bigger external hard drive. I *hoped* that Time Machine would just "remap" the location of the 6GB (or whatever) movie files, without needing to erase old data and copy in a "not-really-new" 6GB movie file. I *suspected* that it would indeed rewrite that, and I'd lose a lot of the Time Machine deep archive. My backups did go back a year or more, but I suspect now I'll only be able to go back a month or two.
Have I missed a simpler way to do this? Too late now, but it may help anyone else who stumbles across this thread in the future - not that that's likely the way Apple's forums now seem to stymie search ... (Original situation: 2TB external drive for media that was totally full; 2TB iMac at around 1.5TB, with 500GB of that also media that I'd rather have on an external drive; several 6TB Time Machine backup drives. New situation: 4TB external drive, that now has all of that 2TB of media plus another 500GB or so from iMac, same 6TB Time Machine Drives.)