Hi Pure_Sinistur,
Have you tried a different controller to eliminate that as the cause of the problem? While I'm on Xbox rather than PS5, one of my controllers has drift, so sometimes my character or vehicle will turn by itself.
You could also try changing your sensitivity or dead zone settings in case that helps. It might also be worth trying it wired and wireless to see if there's a difference.
I'm thinking this is some sort of anti- cheat check. That's the only justification I can think of. Also, I'm on PS5 using a Dualsense Edge controller.
I don't think it'd be this since EA Javelin doesn't run on consoles, and I can't see Sony having an issue with your using an official controller, unless it's going through something like a Cronus Zen.