Steam is emulating the Ps5 controller to look like a Xbox controller. Ps5 controllers use the DirectInput API, but Battlefield only supports XInput API which is what Xbox controllers use.
You can try using a different Xbox controller emulator app such as DS4Windows and see if maybe it works better than Steam's Xbox controller emulator. You'll probably need to disable Steam Input so the two emulators don't conflict with each other.
https://smackstudio.com/how-to-disable-steam-input-controller-configuration/
