First, metrics. When you click the button, they get a signal that someone has been reading the page.
Secondly, there are a lot of JS APIs that require human interaction before you're allowed to use them, for privacy reasons. By clicking a button, those are "unlocked" and they can send all your privacy-obliterating data back along with their metrics.
That's how :(
The publishers want money, just to pay their bills.
Or a specific search term for this interaction requirement phenomenon? I tried the obvious searches, but got lots of false positives in the results.
I am asking as a non-web developer who cannot resist rubbernecking at the incredible dumpster-fire-on-a-trainwreck that is web privacy.
It changes radically between browsers, and browser versions, even before you get to user settings in those browsers that can change it further.
Pro-tip: you can probably block these tracking JS APIs by disabling JS, using NextDNS, setting up a Pi-Hole, or usinf uBlock Origin.