My roommate found a Logitech M525 mouse, that presumably a scavenger took out of a bin & forgot to pick up off the ground (since it wasn't cracked like it had been tossed out of a bin). It was a bit gunky, so I cleaned it up. 2 Amazon AA alkalines inside that hadn't leaked yet, tested them: 80% capacity.
Probably didn't have a receiver next to it on the ground, or my roommate just didn't see it (figures, they thought it was like-new despite the gunk I saw). But I did have a Logi Nano receiver, that I think I found in a giveaway box years ago, saved in case I ever found a Logi wireless mouse to pair with it. Now, the M525 is a Unifying mouse, so it would not natively work with the Nano receiver - yet in Logitech Control Center, the M525 showed up as a M310 (IIRC) while the battery level wouldn't display & movement/clicks weren't detected. But...
After many more-complicated-than-they-needed-to-be iterations with Gemini pushing Solaar, ltunify, a nonexistent GitHub repo "hidpp-pair", and logi_tool, finally concluded with "pure Apple C code" (after a bunch of iterations just by itself):
https://github.com/TheButterZone/logi-nano-pairAnd now, the found Unifying M525 mouse works with the found non-Unifying Nano receiver. Just no customization of all 5 "buttons"; will have to use Mac Mouse Fix for that.