Random Misfire Issue

Hi all!
I’m new to this forum but have an issue with my 2019 Jeep Cherokee Trailhawk that NO ONE can figure out. It has been to 3 different Jeep dealerships and multiple “ma and pa” mechanic shops and no one has been able to solve this.
So what I’ve noticed is ONLY in the winter my car has random misfires while idling only. Once I start driving it stops and will come back when I’m either parked or at a stoplight. The check engine light will either pop up with a message to “service stop start system” accompanied by the A with and arrow and exclamation point or just the check engine light will start flashing. The codes that are populating are P0300, or P1129. First time I had this issue was a little over a year ago (2021) around December and it only happened once last year and now this year it’s happened more times that I can count. The dealerships say bring it in but then they turn the car off and everything stops and when they turn it on they can’t make the misfire happen again so they say to come pick it up. From all the times it has been happening they have recommended I get an oil change, switch gas, get a new battery, flash my O2 sensors, reset the PCM, flash the system for any updates, and change my spark plugs and coil packs or have just said they have no clue and sent me on my way. I have done all of the maintenance listed above but my car still continues to misfire and none of my mechanic friends, or the shops can figure this out.
I was just curious if anyone on here has any more ideas on what it could be.
I have attached photos of what happens during the misfire and what pops up on my screen. I don’t know why but it’s not allowing me to upload the videos of it. Thank you for any responses and ideas!