I am also having this issue, I used to be able to use my PS5 controller with bluetooth and then when it ran out of battery, I would just plug it in and it would work fine. If I disconnect from the wire (after charge), it instantly connected back to bluetooth. Now, FFXIV will detect that the wireless controller exists but inputs aren't received by the game. The controller is only detected through a wired connection. This is very frustrating since I would not like to use third party software or Steam because its not a direct PS5 connection. They will mask it as a XBOX 360 controller and reskin it to a ps5 controller which is something unideal.