Would anything happen if everyone on the planet jumped off a chair all at the same time?

No, because assuming a distribution that is nearly equal, the forces would oppose and cancel out. Suppose everyone one in the eastern hemisphere stepped off a chair because jumping would mean they would impact at different times plus all the chairs would have to be the exact same height. The simultaneous impact would probably be detected on seismometers but would still be such a small amount of mass compared to the earth, that would be it.

Suppose 3 billion people each weigh 100kg which is far more than they would. That is 3x10^11 kg. What is the mass of the earth? It is a little less than 6x10^24 so that is 20 trillion times more. Thus puny humans can jump up and down in unison all they want and NOTHING will happen!

Under the terms of the fundamental law of action and reaction, it could nothing occur: every one is part of the planet ‼

probably a bunch of people would break their legs

There would be many empty seats.