I was able to get FFXI to run on an M1 Mac Mini on Big Sur with CrossOver 21.1.
For what ever reason, it only seemed to work if I installed a Steam bottle first, and then installed the game through Steam. Once installed, I didn't need to open Steam again - you can find the files in the Library folder and launch the game from the Play Online Launcher. It was laggy in the Mog home but I have a ton of furniture. It has a slower frame rate in town but it's playable. Outside of town it ran well, still not as good as my friend's window machine but battles weren't an issue. So, not perfect and a weird workaround, but I had fun playing with friends again. I'm not a big tech person so I'm not sure why it worked through a Steam bottle but crashed every time on loading when installing it in its own bottle. Maybe I just set up the bottle wrong.