I've tried turning down the steering sensitivity, but no dice. I've been running on foot, or trying to see if I can get Jackie/NPC to drive. If not, I'm just creeping along on the highway, probably getting laughed at by NPCs
I've had a lot less problems driving motorcycles. The steering issues for KB+M seem really bad with cars, but motorcycles are much easier to handle. As soon as I could obtain a motorcycle I just used that as my primary transportation for my first time playing, made the game a lot easier.
There's one you can get from a sidequest that follows up on one of the major early plot points (won't say more due to spoilers). Takes a little time but it's worth it.
EDIT: There are apparently two others that come from quests as well, though I can't remember how far into the game they are.
Honestly, exploring the city on foot is pretty fun. I did a lot of my early game traveling on foot, just soaking everything in. You see a lot of neat details you would otherwise miss by driving.
I would play on PC with keyboard and mouse EXCEPT when driving. Then I would pick up my DS4 controller because the joysticks work better for variable input with steering.
In addition to the other advice, also turn your graphics down, it seems like the keyboard steering smoothing happens on a frame by frame basis and just doesn't work well generally, but the lower your framerate is, the worse it gets.
Before the "upgrades" to driving, it was all about picking the right vehicle as only most of them felt like that. But now everything but a bike feels awful to drive.
Before they removed it, the best way to get around was to just sprint, slow time, jump and then bunny hop to gain infinite speed.