They do appear to move a little towards the side of their lane, though they still stay in their lanes. Much like people do when they see a police vehicle or ambulance approaching at high speed. Not entirely unreasonable considering they have a car approaching from behind at high speed, but you are right in that the cars definitely seem to make an effort to avoid collisions.
I am not seeing the car stopping at the green light, but from what you describe I would do the same if I was uncertain an aggressively approaching vehicle would respect my right of way. I would rather let the other guy make an illegal turn than insist on my right of way and get t-boned.
My guess is that it is a small tweaks to traffic the devs have come up with to make the player less likely to constantly collide with other cars when driving over the speed limit. It gives you a little more room to overtake while not making the cars outright pull over to let the player pass. I remember in the early GTA's riding a motorbike was basically suicide since you would inevitably hit a turning car without time to avoid it, while in later GTA's cars would drive more "predictably" around you to make the game flow better. Seeing my Cyberpunk character flying out through the windscreen would be fun the first dozen or so times, but having to respect the speed limit to avoid constant accidents would put a dampener on the "cool" of driving fast cars.