when did clapping become the ubiquitous way for people/crowds to express appreciation?

I can speak to the theater but not to sports/politicians/Americlap.

Theatrical applause in the Western world is reportedly as old as the theater tradition itself (meaning theater of the Greeks), which is kinda insane to think about. "Applaud" entered English from Latin. You slap your hands together just as the ancients might have, though they did other stuff too. But every time you go to any sort of theater in the West you take part in the oldest continuing ritual theater has, which is rather lovely to think about. It's also a collective action, if everyone is clapping it is very hard for you not to clap along, and if you start clapping and no one follows, you knock it off. It's typically everyone or no one with clapping. However, it is maybe one of the least examined aspects of crowd behavior when looking at the history of the theater. The Oxford Encyclopedia of Theatre and Performance dedicates a whole 4 paragraphs to it, though claquing oddly gets 3 to itself. But I can tell you more what an 18th c. London opera attendee got for a snack than I can tell you about when exactly in the opera he might have decided to clap. The simple reason for this is, clapping is but one behavior of many he might have engaged in to provide feedback to the performers, among booing, hissing, just straight up yelling things (good and bad), throwing things on stage (bad things like vegetables but also good things like poems and roses), and demanding immediate encores of favorite arias right in the middle of the opera. Crowd behavior, when it is talked about, usually focuses on telling us about these behaviors as a whole, not exclusively clapping.

So it's actually very telling that you've chosen the word "ubiquitous," because, of all the crowd behaviors that have ever been acceptable at the theater, the humble clap is really all that is left to us now, so it has become very ubiquitous. You have 1) clapping 2) clapping and wooing 3) standing ovation 4) clapping in a low-effort way to show mild disapproval. You really can't even get away with not clapping, and believe me, I've been to some performances where I've tried. Outside of a few noble hold-out theaters, you cannot boo and hiss, you cannot shout your feelings about the performance right in the heat of the moment, and absolutely you do not throw things at the poor performers, though you do see throwing flowers at lady performers referenced in movies/cartoons. (Throwing nice things, however, has one curious but charming survivor, which is figure skating! Next Winter Olympics take note of all the teddy bears and roses thrown on the ice, and consider their historic importance.)

The quieting of audiences from ancients through the 20th century is a very complicated story, with different theories on why it happened, how it it happened, who did it, where it spread from, and even on when exactly it happened. But consider one man's passionate plea for booing at the theater, where he blames the death of rowdy crowds on patrons becoming discerning customers, and customers wanting to reassure themselves they made a good economic choice by attending this particular art event (as enjoyment is subjective), and therefore, we stand and clap at the end of everything now, to applaud not just the performers, but also ourselves.