Yes it does. Use the screenshot, screencast and remote desktop XDG portals for that.
In my use case, I want to screen share a specific window, not the whole screen; this is functionality previously provided by a third-party X11-based tool, which cannot be provided from an XDG portal (even on those compositors that support portal at all).
However, their implementation is not meant for native applications and are pretty inefficient. For example, the screenshot portal will save the image into disk and return its path -- so if you wanted to render the image on screen, you now need to read and decode a file. The screenshot is encoded, serialised to disk, serialised FROM disk and then decoded again just to get pixels from the compositor back into the compositor.
Portal really don't make sense if you're writing native wayland clients, since portals just really end up using the wayland protocol under the hood, with two or three services in the middle handing messages over just to expose a "standard" API.
Regarding the fact that GNOME doesn't implement a lot of functionality: I don't think it's fair to criticise the protocol and architecture because one implementation decides not to implement a given feature. This is like saying "C sucks because some specific compiler doesn't support the feature I need". It's the compiler you've chosen that sucks in that case, not the language.
I'm sure there's some X server implementation out there that's also lacking features you want -- but you wouldn't blame the protocol itself for that implementation's shortcomings.
You mentioned shotman, but that isn't even a real screnshotting tool: it's just a screenshot GUI that depends on existing functionality that may or may not be present in your compositor.
If all the compositors actually supported a standard for providing this functionality; and if that standard provided enough flexibility to do what I want, then I wouldn't complain. That's the essence of modularity. But the standards are poor and poorly-supported, and I literally can't do what I want. Your trivial example of using the sleep command to simulate delayed capture doesn't address the actual issue, and fails to recognize that no amount of hacky solutions will allow me to use a VNC screen sharing tool that shares only a specific window, because the Wayland compositors have chosen not to support that feature and failed to provide a standard way for external tools to do so.