A session that stops running while it is not the selected session arms a
green 'done' reminder dot on its sidebar row, so the operator notices a
finished background session and returns to it; opening the session clears
the dot, and a re-run re-arms it on completion.
SessionManager owns the reminder set (a sibling of the waiting-approval
bit): a running->idle edge of a non-selected session arms it, select()
consumes it, removal prunes it, and it survives connection generations.
The bit rides SessionListEntry/SessionSummary into the workspace browser
rows, which render the existing StateDot done state (running keeps the
spinner) and label the hover card '已完成/Completed'.
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