I suspect they're referring to the fact that after the Zoom app is updated, you may find yourself in a meeting but unable to share a window because the updated app no longer has the "Screen Recording" privacy entitlement. Turning that on again requires quitting the app and therefore leaving the meeting.

This is exactly the issue. It's especially problematic when you are hosting a private meeting. When you exit, it will hang up on everyone, unless you hand control of the conference to a participant.

That does sound annoying. Though to be fair, Apple has plenty of reason to distrust Zoom updates. I'm a bit surprised there's no way for Zoom to re-try screen recording without re-launching the app. Is that a fundamental limitation of Apple's security model, or a failure of Zoom?

It is all Apple. When you change a permission, MacOS forces you to quit and re-launch the app.

It's also all-app: they can change their homemade updater to a normal non-hidden updater and have normal signed distribution that doesn't require any of this re-auth.

Not a strange claim. Having to exit the conference to give the Zoom app permission to share the screen is painful, and if the Zoom app updates, you have to do it again. That means you have to leave the conference to permission the app, and if you are the host, hand off control to a participant so the conference is not ended early.