Where exactly does Finder store an iPhone backup file?

The name of the actual directory changes, but you should be able to find it with the iPhone page in Finder and "Manage Backups". It should give a list of all iPhone and iPad backups and you can right click on "Show in Finder" to get the locations. I see them at /Users/<username>/Library/Application Support/MobileSync/Backup

And yes the backups should be available by using a Time Machine backup, but I'm not sure how it's done other than restoring from the Time Machine backup and then Restoring from the iPhone backup.

And that's for bringing it up because for some reason I had about 8 old backups of my iPhone and I'm not sure why. I freed up about 100 GB by deleting 6 of them.

This article will tell you where your backups are stored→Locate backups of your iPhone, iPad, and iPod touch - Apple Support

Note that if you go to Manage Backups in Finder you can archive a backup; right click on it and choose Archive. That will preserve that backup, and the next backup will create a new one. You can save as many backups as you have space for.

Also, when you update iOS, the next backup will create a new backup, and the backup made before the update will be archived.

Twelve Shades Publications wrote:

My troubles began when I find only one backup in the list of backups in Finder: only the most-recent one that was taken!

Which of course makes utterly no sense to me: "what good is that?" (Monterey latest, iOS latest.)

All of my other ones (other than the latest) were manually archived by right clicking on my latest backup. If you never manually archived a backup, only one will stay there long term. Backups are also incremental, although each backup directory is self-contained once the backup is completed. I believe there's also a mechanism that reduces the chance of corrupting the archive should the backup process be interrupted. But for the most part, the idea is to not waste storage space unless the user specifically wants to devote such space to an archived backup.

Twelve Shades Publications wrote:

Well, that may be so ... but all that I can really say is that I am terribly disappointed with this set of Apple engineers, given the utter thoroughness with which the Time Machine team had solved exactly the same problem. "It is the very least that we should have been able to expect of you" that you could have managed to save more than one backup.

Time Machine is designed to do multiple incremental backups where the backup files can be parsed to recover from a specific point in time. iOS backups have always been individual, independent directories, but ones that can be archived at the request of the user, but with a storage penalty. That's always been the way it's worked.

that is how backups on the Mac have always worked. There is one backup that is replaced each time you backup your iPhone. iCloud is the same way.

If you need to keep a certain backup, then you have to archive it.