Nah the Chinese are smart enough to not shoot an air to air missile at Pelosi's plane. That would be a legit act of war to kill the 2nd or 3rd highest leader of America.
America would start a small scale naval/air war if that were to happen. The pretext of this small naval war would be "Chinese aircraft engaged American naval aircraft conducting patrols". After a bunch of air to air engagements between China and America, hostilities would cease soon after when China starts deploying its hypersonic carrier killer missiles. Then the world would enter into a dark age because all economic ties between America and China would be cut off. The American navy would takeover all trade routes to prevent any shipping headed to China. If America penetrates Chinese airspace with F-35s and starts killing civilians, then yea, the world would get into a Cuban Missile crisis like scenario where the world awaits nuclear winter. Mass rapes, killings, starvation, cannibalism, and mass looting will be commonplace during the nuclear winter. The world would reset. The elite billionaires will have armored and mobile killer AI robots protecting their bunkers.
The luckiest places to be during this time are remote places in Burma, Nepal, Canada, Alaska. If people see your smoke from your fire in the woods, they are headed towards YOU and your homestead. They will scout your place and devise plans to assault your cabin when you are asleep.
Anyways... China knows that it is much more powerful now than in the mid 90s where they couldn't do jack squat when an American aircraft carrier showed up at the Taiwanese straight. But still, they know that they are not quite powerful enough yet to take on the American navy.