@ivun3 that smoothing and ramp up of the input is precisely what that new steering assist introduced in F1 23 aims to achieve. There's a toggle somewhere in the game settings, have you tried disabling it?
It's an accessibility feature so to speak. Aims to aid elevate the gameplay for most pad users, but you seem to sit outside their intended audience with your skills - that's commendable, by the way ✌🏼
If disabling it does not cut it for you, then indeed we'd need to sit out some hidden line in the game files. I don't have F1 on PC, but if you manage to link me to a copy of the many editable settings files (on a DM preferably) I can give it a try. We do that on iRacing all the time!
Bear in mind that they may be in a different file than the one you used to tweak your graphic settings.
Regarding the 360 idea,
@ScarDuck14 is right as far as I know. It's been explored before, but no implementation have been made due to the idea not translating as easily as we imagine. You can sort of tweak that in by messing with the linearity and saturation settings for the steering, making it so that those last degrees of the 180 range you already use ramp up to cover higher input angles, but a proper 360 range have never been successfully designed out to the best of my knowledge.
Not that it's not possible, just that it doesn't fit how the majority of players use their pads so it's hard to justify even as an alternative control scheme.
The best implementation of an alternative control scheme for pad users I know is the GT7 approach with the gyroscopic capabilities of the Dualsense and Dualshock 4
Oh, and I can vouch for the thumbstick accessories Duck is referring too! I used them a lot before getting a wheel and loved them!