It was set to chill.
I am not aware of that driving rule. I always turn into the right lane at that intersection. It is a T intersection with a traffic light. Traffic is stopped. I don't see why you would need to turn into the left lane first.
One reason that might be enough to codify it is that humans function better with habits. Much like people who don't normally signal but say "I always signal if there are other cars" likely fail to do so far more often than they realize, a person who "would use the left lane if there was an oncoming car turning right" may not see such an oncoming car, in which case an accident or evasive maneuver could have been avoided with basic defensive driving practices. Even when approaching a T intersection like this and recognizing that it is different, having an additional habit could just be one more chance to activate the wrong habit when distracted elsewhere.
California permits a left turn into any lane WHEN SAFE TO DO SO. A protected left turn on an arrow would typically have a no right on red sign on the opposite side of the intersection. But the left turn has the right of way in this particular situation, so the car making the right would likely be at fault because he/she is turning on a red light.
I can't say for certain whether or not you are wrong about California, but usually when I see a "no turn on red" sign it is because of the visibility of the intersection (sometimes it might be about the amount of traffic typically present, and then there is ofter a time limit tied to the sign). Outside of those scenarios, in Indiana, we definitely have plenty of intersections with left green arrows for one direction of traffic that don't have "no turn on red" signs for the other.
I was behind a truck pulling a boat at a stoplight. FSD stopped correctly behind the towed boat. I disengaged FSD and pulled a little forward to tell the driver in the adjacent lane their trunk was opened. When I re-enabled FSD the car started to drive forward, I had to disengage with the break. The on screen visual now showed no vehicles in front of me (could not see around the boat and did not recognize the boat as a motor vehicle).
While a boat may be a vehicle, and this boat may have had a motor, I'm more concerned that FSD didn't recognize and remain stopped for the obstruction than I would be that the visualization didn't show it. While getting rid of radar sounds sensible to me, this seem to indicate that vision without radar may not be as far along as I would have anticipated.
Currently my biggest "small item that bugs me" is if there's no lane painting on the right side of the lane, it'll drive way too close to the right side edge. Many places here have some bushes and stuff and I'm afraid it'll scratch the car one of these days.
Strange, I have the opposite problem on a road I drive on daily. It's a pretty narrow road, and my X frequently drives on or acts like it's going to turn over the double-yellow instead of driving closer to the edge as it should.
I will try different coming from a different direction. But I will point out that once you complete the turn, the front cameras will have a clear view of the speed limit sign. So the car should immediately slow after the turn as soon as the front cameras see the speed limit sign but it continues to drive past the speed limit sign at the same speed. I specifically noticed that the speed limit on the screen does not update after the car passes the speed limit sign.
The visualization should show speed limit signs, and if it shows them, it should show the speed detected on them. Take a look at it and see if it shows them, then you'll know if it's misreading them, missing them, or overriding them after the fact.