No, not really. In practice what happens is Discord/Zoom/etc do implement it for the most popular compositors and then the other compositors follow suit if they want to support those applications. You would be complaining even more if they only supported weston because their screencast mechanism is pretty limited, and it would suck if the other ones just copied that.
The current "standard" is to just use pipewire and have the display server talk to the pipewire server, most commonly using xdg-desktop-portal. This is obviously outside the scope of Wayland, because any application can talk to pipewire and share/receive a video stream. I don't know about Zoom, but Chromium has support for this in the works, so Discord should get that eventually from updating their Electron: https://github.com/electron/electron/pull/26022
I'm not fully up to date on the state of these things, but if the different implementations doesn't have a common interface it's goodbye to ever having screensharing work for everyone. I think that's what the parent means.
If we're lucky Discord/Zoom/etc. will implement it for the most popular compositor(s).
Similarly with screenshots - even though it's a much simpler problem it's annoying if the program taking the screenshot is fundamentally bound to a specific compositor.
If I'm not mistaken there are standardization efforts underway today though?