I only have Fedora 37 on my FW13, so no dual boot here. I also have just one fingerprint registered, left correction, right index finger.
I see only one file, at /var/lib/fprint/<user name>/goodixmoc/<some UUID>/7.
I’m guessing that fprint (or the goodixmoc driver) is counting fingers left to right starting with 1 for the left pinky.
I managed to move the fingerprint registration between Fedora installs on different SSDs back in the F35 days, when I believe libfprint wasn’t able to delete fingerprint slots from the reader, by copying the files.
That’s worth trying between fedora and Ubuntu here. Another thing to try is to maybe register a different finger on each Linux install?