Hello my 2021 5.3 AT4 shakes also… I noted it after doing the K&N CAI and exhaust..
then at 8127 my # 6 lifter blew .. after repair it just shakes all the time while going slow!
I return it to stock filter and it got 80% better but now with Air conditioning on it is more noticeable. A/c Off near perfect
I don’t know but Dealerships say it is operating to Spec but I doubt it.
during lifter warranty work they also replaced #1 cylinder plug for misfiring and it was fouled. So I will soon be going to Mobile 1 oil and all new plugs hopefully this helps