Hey new player here. I have the Steam version of FF14. I bought the X Series controller to play Final Fantasy with. Was having the same issues everyone described here. Good thing I found this forum post. Anyways, I just exchanged the controller for one of the older ones and it works fine over Bluetooth for me now.
On a side note, the X Series controller would randomly disconnect from my laptop for a few seconds every now and again which was annoying, the older one isn't having that issue. I think its probably connected to that new Bluetooth protocol someone was talking about earlier in the thread.
Not the ideal fix, but I think I prefer having a micro-usb to charge my controller with anyways.