Yeah, it's really the strangest thing. I have tried other games I have on Steam and they don't have this issue. I also did try downloading and installing the launcher directly from https://www.finalfantasyxiv.com/ and that launcher does indeed work fine. I don't know how to fix the Steam launcher, and it doesn't appear that others who run the game through Steam have the same issue, but at least I have a good workaround.