x11/session: Set the context as client data on connection watch

Merged Jonas Ådahl requested to merge jadahl/mutter:wip/fix-ice-shutdown into main

It was already assumed to be the context, but we never set it as such, so things just crashed instead. Now when we set it up correctly, hopefully that won't happen anymore.

Closes: #2406 (closed) Closes: #2267 (closed) Closes: gnome-shell#5078 (closed)

Merge request reports