Documenting this with better search keywords so it’s easier for me to find next time.
I re-installed FFXIV on my new PC and of course all of my settings were gone. I dimly remembered running into this before, but it took a while to dig it up.
To copy your FFXIV settings from one machine to another, copy Documents\My Games\FINAL FANTASY XIV – A Realm Reborn to the other machine. I left out the “screenshots” and “downloads” folders.