With Crossover 22.1.0 we get 32 bit support, so I was able to get the launcher to open and update!
Unfortunately, I still haven't been able to get in the game because when hitting load screens, the 'patching files' text appears and any updates that need to be downloaded are done extremely slowly. The text itself even says 0 bytes per second, but in the load screen you can see the progress going up ever so slowly. I waiting for almost twenty minutes before I gave up and exited the program. Not sure what could be causing the slow downloads for these updates as this wasn't an issue previously on Crossover. But at least progress is being made :)