feat(frontend): shared pod-wide test audio

Make the "Test audio" connectivity check pod-wide instead of local to the
publisher. Shared on/off state is derived from the presence of the podman-beat
track across participants (self-syncing on join/leave). Any participant can
stop it: the owner unpublishes directly; non-owners send a new additive
BEAT_STOP data message that the owner honors. Drives the button label, status
line, and status waveform for everyone, and guards against rapid-double-click
double-publish and mid-start unmount leaks.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

docs/test-audio.md

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+# Shared Test Audio — pod-wide connectivity check
+
+> Spec for the `frontend/src/livekit/useBeat.ts` + `PodView.tsx` test-audio
+> behavior and the additive `BEAT_STOP` data message. Satisfies the
+> documentation-first gate for those files.
+
+## Why
+
+The **Test audio** button is PodMan's pre-flight check that the LiveKit audio
+path works for the whole pod — the same path the urgent Gemini-TTS voice
+escalation rides on. Today the beat is published correctly but its on/off state
+is **local to the publisher**: teammates can't see it's playing and can't stop
+it. This makes it a shared, pod-wide toggle so a judge sees the state flip on
+every screen at once.
+
+## Behavior
+
+- Any participant clicks **Test audio** → they publish the `podman-beat` audio
+  track (Web Audio, `lib/beat.ts`). Everyone auto-subscribes and hears it.
+- The shared on/off state is **derived from the track's presence**, not a synced
+  flag — so it self-syncs across joins/leaves and can't drift from reality. The
+  publisher is the **owner**.
+- Anyone can stop it:
+  - Owner clicks **Stop audio** → unpublishes its own track directly.
+  - Non-owner clicks **Stop (`<owner>`'s)** → sends `BEAT_STOP`; the owner
+    unpublishes. (LiveKit forbids unpublishing another participant's track, so a
+    request is the only way.)
+- The Status card shows `publishing` / `<owner> playing` / `ready`, and the
+  waveform animates (`active`) for everyone while the test is live.
+
+## State derivation (source of truth = the track)
+
+`useBeat(room)` returns `{ on, by, mine }`, recomputed from the presence of a
+track named `podman-beat` across `localParticipant` + `remoteParticipants` on
+these events: `LocalTrackPublished/Unpublished`, `TrackPublished/Unpublished`,
+`TrackSubscribed/Unsubscribed`, `ParticipantConnected/Disconnected`. Owner
+disconnect and late-join sync therefore need no extra messaging.
+
+## Contract (additive)
+
+`shared/src/messages.ts` — one new message on the existing `podman.intervention`
+data topic:
+
+    | { type: 'BEAT_STOP' }   // any participant → owner: stop the shared beat
+
+Additive to the `DataMessage` union; existing consumers ignore unknown types.
+**No backend / API change.**
+
+## Known limitation (LiveKit constraint)
+
+A client can only unpublish **its own** tracks, so a non-owner's **Stop** is a
+`BEAT_STOP` _request_ the owner must honor. If the owner disconnects **uncleanly**
+(crash / network drop), the SFU keeps the track published until it times the
+participant out — during that window the beat keeps playing and non-owners can't
+stop it. A clean disconnect clears it immediately via `ParticipantDisconnected`.
+Demo mitigation: have the same person who starts the test also stop it.
+
+## Files
+
+- `shared/src/messages.ts` — `BEAT_STOP` message (additive).
+- `frontend/src/livekit/useBeat.ts` — `useBeat(room)` hook.
+- `frontend/src/components/PodView.tsx` — button label, status line, waveform
+  `active` driven by the hook.
+- `frontend/src/lib/beat.ts` — unchanged (existing Web-Audio beat source).