Update: Turns out initial theories about it being a Unicode problem were correct, with Square Enix saying it's managed to fix the issue in a Lodestone post. The game was having a bit of a tantrum if you try and link your accounts with any special, non-English characters in your Steam profile name.
Why it doesn't pull from your account name instead is beyond me. It also feels strange that it came down to this issue considering the game's large Japanese player base. but according to Square Enix everything should be fine now. I did spy some people saying they were still having issues despite having no special characters in their name, but a fresh install should fix that problem.
Original story: A huge portion of Steam Final Fantasy 14 players are finding themselves unable to log into the game after new security measures have perhaps made the game too secure.
The game just went through a lengthy maintenance period, intended to implement some hotfixes and change the way logins work for Steam users. It means anyone who purchased the game through Valve's client is now required to link their Steam account to their Square Enix account.
It's supposed to be an extra security measure, but it was already causing some concern in the community—not everyone wants Steam running in the background 24/7 and people had already anticipated for it to mess with some quality-of-life plugins pretty heavily. But right now, the biggest issue seems to be that the new system has broken the game for Steam users entirely, with the vast majority unable to get past the login screen.
Attempts to log into the game will throw up a "technical error" message, with no other option except to force-quit the game. One issue seems to be around the use of special characters in Steam profile names. I was having the issues myself, but changing my Steam name to standard English letters allowed me to finally link my accounts. It doesn't appear to be working for everyone though, with other unknown issues yet to present themselves. One Reddit user has said that Square Enix support is aware of the issue and that it's on their end, with a proper fix hopefully coming soon.