Turns out that there's no standard tag for this, but the most common (from what I searched was POPULARIMETER, where you store it in EMAIL|RATING|PLAYCOUNTER format. Email is a string (optional), rating is an int 0-255※, and playcounter as an integer.
So I wrote a Python script that would read the file on disk, match it with the entry in iTunes DB, populate POPULARIMETER, then verify everything was set correctly in MP3tag.
This took a few hours to do, mostly due to discovering how to do it and verifying everything worked correctly. Unfortunately the MP3 players I use now (VLC and mpv) don't support updating the POPULARIMETER field, so it'll be left as an unchanging relic from my iTunes days.
※ - 1 star → 0.2x255 = 51, 2 star → 0.4x255 = 102, etc