Nintendo Switch Pro Controller joystick drift in wireless mode?

I received my Nintendo Switch Pro controller today.

Unfortunately I have the problem that the character in Animal Crossing New Horizons moves very slowly down to the left when I have connected the Pro Controller in a wireless state.

That makes the game unplayable. All other games run without problems with the wireless state.

Now it comes: If I connect the Pro Controller to the switch via cable and reconnect the controller, I no longer have a problem in Animal Crossing.

Problem: In the wireless mode of the Pro Controller, the character automatically runs slowly down to the left.

The question now is: is the controller defective?

Maybe it's the game