Not Square-Enix support, but I'm going to chime in here (sorry, Dynratygus)...

FWIW, on the M1, the system will take Intel applications and create ARM versions of the executables; it does this on first launch and then caches them (Ahead-of-Time compilation, or AoT) as opposed to doing it on the fly while things are running (Just-in-Time compilation, or JiT). This is why it takes a while to launch an Intel app the first time, and then it launches very efficiently until a new build comes along, at which point it recompiles.

As best I can tell, the way the Crossover bottle does things with its happy little preloader (and all the actual FFXIV installation in a support directory), it does not actually show up as a different version after the launcher updates things, and so MacOS happily tries to use the previous AoT-compiled version on the new executables... and thus seemingly horks up a hairball.

The practical upshot is that the game will stop launching on M1 ARM Mac systems after the first time it updates.

The most effective current workaround seems to be going into the Crossover bottle and deleting the wine64-preloader component which apparently causes the problem: either go to the command line and simply move into the FINAL FANTASY XIV Online.app directory (.apps are functionally directory structures on MacOS), or select the application in Finder, then right-click/control-click and pick 'Show Contents'. Once inside the app either way, delete the SharedSupport\finalfantasyxiv\bin\wine64-preloader file, and then run it again; without the preloader, it seems to figure out that "hey, this has changed" when you run it.

(Or if you want to play it really safe, just move the wine64-preloader file somewhere else in case you have a reason to put it back later.)

Long term, there's probably a better way to handle it, but in my experience that should get you back up and running for now.