Check out the wiki pages on the
Revolution, as well as the various revolutionary govenment reforms for republics and monarchies. (You can skip the detailed descriptions of events, but the editorial parts seem helpful.) You'll probably need to read it several times to understand what's going on. (At least, I needed to read it several times, lol.)
So far, I've always come to the conclusion that it wasn't useful to me to join the revolution, but that decision will always depend on your specific situation and goals. (As this is very lategame, it's difficult to give useful generic advice.)
It's a bit of a pain that the center of revolution is in your lands but Austria is the revolutionary target, because I think that means that the only way to remove the revolutionary influence is to deliberately spawn the disaster, side with the monarchy, and win.