[ZHSD001A]

Wondering if anybody experiencing similar engine shudder issues. I own my 19 X3 M40i since last August and It started to develop this issue a month ago. The engine will shudder for 1-3 seconds, 2-5 seconds after it restart from the auto start and stop function. Yes I drove around a parking lot and use the stop watch from my phone to time the vibration I can feel the shudder under my seat even not touching the steering wheel. Gears are in Drive and auto hold are engaged which means engine is at idle when the shudder occurs. It does not shudder at all when I turn on the engine by pressing the start button though.
Another issue with the engine is idle vibration felt through the steering wheel. Whenever it idles, I can feel a slight vibration through the steering wheel. As soon as the rpm just raise a little, that vibration disappear. Once or twice I don't feel the vibration is when I notice the idle rpm is higher than usual at 750rpm.
It is currently on 35k miles, with engine mount replaced under warranty this April. Oil change was done this July, and software was updated 3 weeks ago from a local dealer.

I have researched previous threads on engine vibration problem related to 2018 X3 M40i, but those happens at driving not at idling. Would like to hear advice on what causes these idle vibration