They messed up the deadzone so you have to use virtual joystick remappings to fix it. Or otherwise you have to wait for them to fix it in a patch
It's not over-steering. It's the rotational momentum which needs to get countered first
In the original games left/right stick would indeed yaw the ship, while holding the roll button (or using twist stick) would roll. This was hardcoded. In 2020 with a HOTAS I agree that it's a bit jarring and I use my pedals for yaw instead.
I don't think they will ever fix the animation as it is in-universe correct. I've not seen the pilot use pedals at all, his/her feet just sit there. Rolling is more of a "cool" thing in Star Wars and all ships seem to be facing the same way up. Space also doesn't behave like space. Well, except in The Last Jedi... But let's not bring that travesty into this.
Deadzones are a problem, though on my stick I only seem to have about 5-10% and it's quite playable. Pedals have no deadzone.
MSFFB2 (with simFFB)
X52 Pro (throttle only)
MFG Crosswind v1
P.S. I would love to get some rumble on my FFB stick.
