Ime, the jerk was resolved by TCU updated and PCU updated.
The OP references a 2022 model. I believe the TSB you reference (attached below) is the one intended to resolve a jerk-jerk in low gears applying to 2020 and and some prior, not 2022.
My experience with that TSB is a little bizarre. I had that TSB applied at 8,000 miles though the issue I was trying to resolve was lugging, not jerking. It certainly helped with lugging, the instances of that sharply reduced.
What's bizarre is that the low gear jerking I had previously noted only once is now increasingly frequent, a single jerk when both slowing and accelerating, downshifting and upshifting between first and second., when conditions require lollygagging. My TSB application was free, why I could not say other than a good will gesture.
This is the umpteenth time + 1 I've pontificated on the subject. That's because this less than smooth low gear shifting is the 1 and 1A issue I have with this vehicle. Otherwise, a great vehicle for this price point.
the 'lurching' thing seems to be an issue on low mileage vehicles that get babied on their acceleration. try flooring it (passed the kick plate) a few times when getting on the freeway to snap the PCM programming out of whatever funk it's in.
I've seen this even happen on new vehicles with under 20 miles on them when they are mostly driven slowly on the lot
I'll give that a try though I'm not encouraged. Mine is not a commuter car. And for three miles in any direction leaving my house I go from stop to 55 MPH, often briskly to 4,000 RPM to get into the traffic flow. It's when I get 3 or 8 miles to the shopping districts with a series of traffic lights, stop signs and lollygagging drivers I notice the jerking most. Regardless, there's no question it's happiest with some zoom-zoom driving when conditions permit.
The last two times out I tried TCF OFF. Early returns say I'm seeing improvement but more testing will be in order. Why this would make a difference would be a headscratcher, maybe slightly less engine load. Some have observed that TCF OFF yields performance akin to a sport-lite. Maybe smoother shifting is what they are sensing. More testing to come.