Haven’t seen any border control either and we cross several borders between Belgium, France, Germany and Austria each year. The only border control I’ve ever seen is in Basel, Switzerland, and even that is never a big deal, they have never actually stopped us.
Some games only work with generic xinput controllers and don’t support the DS4 natively. In that case using the ds4drv with the emulate xpad option can help.
That said, I’d expect a game published by Sony and originally released on a PS4 to support DS4 controllers natively.