I am really puzzled how are they able to "quietly" update the terms without notifying their users? Everybody was joking about the emails (We have updated our terms...) raining from every company when GDPR et al. got introduced. What changed?

I thought those emails were a form of protest, like complying in the most annoying way possible just to make a point.

Possibly they've done something illegal here. Let's wait and see (or, if you're in the EU, take action and report it to your data protection authority and NOYB).

Section 15 of the agreement ("MODIFICATIONS TO THIS AGREEMENT") allows for Zoom to unilaterally change the terms without providing notice other than updating them on the website.

In many countries that is illegal... ToS does not go over the local laws.

In such jurisdictions, it would be unenforceable, but not illegal. The agreement is executed in California per section 33.3, where it is perfectly legal.

You really ought to read “No Filter” by Sarah Frier. She talks about exactly this, except with Apple and iTunes in 2001. Apple’s biggest change wasn’t “digitizing music”, it was enabling a system that allows arbitrary changes to terms and conditions for services they offered. Apparently if you presented a digital copy of a TOS and users clicked one button, it was legally binding. Other companies caught on and started doing it, and well that’s how Zoom is able to do this - people don’t bother to read what they’re agreeing to so legally it’s the user’s fault if the software does something they don’t like.

It's settled, then. I'll move on to using a different video chat service...

They're a dime-a-dozen. Good job tanking your reputation and business, zoom!

I'm sure they'll miss your business, but this change will hardly impact their bottom line. Most users will continue to use it, even if they're aware of and are concerned by this, as the cost and inconvenience of switching is too high.