S1: status chips on the session list — live tri-state over the shared rows #1787

Acceptance Criteria

• A running hub session's list row shows a busy chip; a session with a pending question shows waiting on question; an idle session shows idle with age.
• A session whose owner is unreachable keeps its current status (omitted ≠ idle — absence never resets a chip to idle); the row self-corrects when the owner returns or the row TTLs out.
• Chips update live off the event flow (no polling loop beyond the existing reconnect/visibility-gated re-seed seams).
• Render-only: zero writes to session state, zero engine changes, zero new routes (a discovered state gap stops the slice and gets named, per the parent).
• The chips' status semantics rhyme with the peer-fleet session-status design (fix(fleet): remote session keeps its working rail + tab state after reopen (fleet-aware status re-seed) (#1766) #1768): tri-state busy/idle/omitted, recency-guarded reconcile, visibility-gated self-heal, honest-absence fallback — so the reconciliation lane converges the two lineages later with no translation layer.

Testing Decisions

Extend the session list/store suites and the reconcile-semantics tests; reuse the #1768-style tri-state test shapes (explicit busy settles stale idle; omitted key never changes the store) adapted to the shared-row source. Headless probe for the live chip.

Key Decisions

• Data source is the shared runtime rows (busy + registration, TTL'd) — NOT the peer-fleet session-status route (the hub does not serve it).
• The fix(fleet): remote session keeps its working rail + tab state after reopen (fleet-aware status re-seed) (#1766) #1768 rhyme is a constraint, not a suggestion: same tri-state semantics, same reconcile guards, different data plane.

Constraints & Invariants

• An unreachable owner never blanks a live chip (the rail invariant, one level up).
• No polling: ride existing re-seed triggers (connected edge, sync-gap frame, visibility-gated self-heal).

Prior Art

• P2's shared busy/registration rows and their TTLs — the data plane.
• fix(fleet): remote session keeps its working rail + tab state after reopen (fleet-aware status re-seed) (#1766) #1768's fleet session-status (tri-state map, per-owner honest absence, recency-guarded reconcile, 10s visibility-gated self-heal) — the design to rhyme with.
• The Fan-in relay never re-arms backpressure (flowing stuck false) → session transcript + rail go stale until reload #1617/Client: honor status seq + re-seed status on reconnect/gap + turn-level working floor (non-text turns) #1637 client floors (seq-honor, turn-active) — the state-layer guards beneath the chip.

Source

Part of #1785. Composes after S2 (the question inbox); shares no surfaces with it.

Notes

The live hub answers 404 for every peer-fleet service route today; S1 must not regress that state and must not add a dependency on those routes landing.