Get Rooster Activity

Company OS 2026-09-30 handoff item 6, System -> Rooster's Activity tab (design/Rooster.dc.html, CHANGES.md §7): the status strip plus "Actions taken on his own". See app.modules.rooster.activity's own module docstring for exactly what each field honestly measures and the one design state (a genuine process-down "Not running") this build cannot yet tell apart from "stalled".

"Research cases handed to a person" and "Questions closed unanswered" are NOT in this response: the first is GET /api/rooster/cases/handed (a cases/ module read, kept in that module rather than reached into from here); the second has no backing data source in this build yet (see the PR body) -- the frontend renders its own empty state for it rather than this route inventing one.