While the newer official launcher for FINAL FANTASY XIV Online is incredibly problematic with Steam Play Proton, a third-party launcher has recently come to Linux to help with that.
A game I know a great many people enjoyed, and now that XIVLauncher is properly available for Linux and installable from Flathub, it should allow more people to continue playing on Linux and the Steam Deck. The team behind it even set up a full guide to getting it running on Steam Deck. It even includes a special build of Wine that has been tuned just for getting FINAL FANTASY XIV Online running nicely.
Hopefully at some point it won't be needed, if Square Enix can look at the issues with their official launcher, but once again the community delivers to get a game more easily playable on Linux and Steam Deck. Currently, it has an Unsupported rating for the Steam Deck, largely due to the launcher. So if you wanted to get FINAL FANTASY XIV Online working on Linux and Steam Deck — this is for you!
As always with third-party launchers, use at your own risk.