Wow! I finally got it but it was extremely counterintuitive. I had to go to the Ringtone settings page on my iphone 13 and there was a section with "Store" with two buttons, "Tone Store", and something like "Download all downloadable ringtones from the store".
I had no interest in purchasing ringtones from the store, so I didn't bother tapping this at first, but I figured what the heck, and I tapped the "download all downloadable ringtones", and the .m4r file's ringtone instantly appeared in the ringtones list in settings, and I was able to use it.
It is astonishing that this worked, since my .m4r file was in my Files app on my iphone 13 the entire time, so in no sense did I "download" it.