Same occurrence for me as well, on PC's running both Windows 11 and Windows 10 - playing through the Standalone launcher (non-Steam).
Desktops that are Windows 11 with two different PS4 controllers detect & connect via Bluetooth built-in to the motherboard fine, but XIV does not see them.

Gave it a go on my laptop, Windows 10 with Standalone Launcher, with a completely different controller - same scenario as above, still does not see it.
Final attempt was Desktop Win10 that uses a Bluetooth Dongle as opposed to built-in, with the same result of not seeing the controller in XIV but everything else see's it fine.

All scenarios, connecting directly to the PC via USB cable had them all become seen within XIV simply as 'Wireless Controller.'
Prior to 7.1 they all detected said controllers over Bluetooth perfectly and, in the laptop's case, since I started playing back in Patch 4.3.