bug: RoomPolicy's gate-collapse and operator-docs rules do not suppress live

From docs/reports/e2e-slack-test-2026-09-20.md (N2), the live validation run of the issue-393 room rework on the-loop 19.7.0.

Seen

The rules exist and are unit-tested, but in the live room:

• Each human gate was still announced three times within seconds: the 📋 phase-approval-pending digest with the Approve / Request changes buttons, a 🔨 "X reached gate" line (phase.progress/phase.started), then a 💬 "gate is ready for review" mirror (comment.agent). Only the first is actionable. 9 of the run's 31 bot messages were these duplicates.
• The tmux cheat-sheet still posted to the room (the session-started mirror with the attach table and shell block) — the operator-docs suppression did not fire.
• The endgame piled five messages into two minutes (🎉 at-complete, 🔨 started-complete, ✅ completed-complete, the agent's ✅ summary, 🎉 closed); the complete node's own started/completed pair says nothing.

The transition-collapse and progress-edit rules DO work live (no mid-run phase.completed lines; the six-node review chain rendered as one message edited in place), so the wiring is sound — the failing rules are the ones keyed on recognizing a gate's satellites and an operator-doc mirror.

Root cause (found on the 2026-09-20 follow-up)

Three independent reasons the rules could not fire, all confirmed against the runtime and the mirror path:

1. The gate node emits phase.progress, not phase.started. An approval node declares no phase: of its own and inherits its predecessor's, so entering it does not change the phase label and the runtime emits phase.progress. Gate-collapse only dropped phase.started, so the gate's lifecycle line was never a candidate to drop.
2. The "ready for review" mirror carries no node. publish_comment derives no detail["node"] from a mirrored comment.agent, so gate-collapse's node guard (if node and gate_ts.get(node)) was always false for it.
3. operatorDoc was never set. The rule read event.detail["operatorDoc"], but nothing ever stamped it — the session-started cheat-sheet posts straight to GitHub and comes back as a plain mirror.

Fix (branch fix/n1-selection-grammar-refusal-reason)

RoomPolicy.decide now: (1) collapses a phase.progress and phase.started at a node with a live gateTs; (2) reads the gate node from the "ready for review" mirror's own text ("<node> is ready for review") and matches it to a pending gate, so the nodeless mirror is dropped for exactly the gate that is open; (3) recognises the tmux cheat-sheet by its own lead ("started an interactive session for" + "tmux attach -t") as operator docs. Plus an endgame-collapse rule drops the terminal complete/done node's own phase pair (the empty "started/completed phase complete" lines) — the dedicated work-item-complete / work-item.closed events and the session's summary carry the end. Unit tests per rule in test_room_policy.py.