feat: couple broadcast to voice + voice-controlled broadcast toggle

Completes the STREAM_BROWSER=true behaviour:
- handleJoin auto-starts the broadcast on voice join and wires the session to
  the guild streamer; each turn reports the live state to the brain so search
  routes Chrome (live) vs Gemini (off).
- New setBroadcast tool lets the user toggle the broadcast by voice ("방송
  켜줘/꺼줘") via the LLM (no hardcoded phrases); it refuses when
  STREAM_BROWSER=false. The directive flows brain -> bridge (broadcast_action)
  -> bot streamer.start/stop, guarded by isActive() so it's idempotent.
- Per-turn IPC uses a thread-local (reply/turn_state.py) instead of threading
  params through the whole engine chain: bridge sets broadcasting in, tool
  records the directive out; Tool.execute exposes broadcasting on ToolContext.

Bot typecheck clean; brain covered by tests/test_set_broadcast.py (+ existing
routing tests). Specs + docs updated.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/jarvis/reply/turn_state.py

@@ -0,0 +1,48 @@
+"""Per-turn, request-scoped state shared between the bridge, the reply engine
+and tools — without threading extra parameters through the whole engine call
+chain (run_reply_engine -> run_tool_with_retries -> execute_tool -> execute).
+
+Flask serves each HTTP request on its own thread and the reply engine + tools
+run synchronously on that thread, so a ``threading.local`` cleanly scopes a
+single turn. Anything that can't see the thread-local (a worker thread, an eval,
+a unit test) just reads ``None`` and the caller falls back to its default.
+
+Fields
+------
+broadcasting : Optional[bool]
+    The live screen-share (Go-Live) state the bot sends with the request. The
+    webSearch routing reads it to pick on-screen Chrome (live) vs Gemini (off).
+broadcast_action : Optional[str]
+    A directive ("start"/"stop") recorded by the setBroadcast tool for the
+    bridge to return to the bot, which owns the actual broadcast.
+"""
+
+from __future__ import annotations
+
+import threading
+from typing import Optional
+
+_state = threading.local()
+
+
+def reset() -> None:
+    """Clear per-turn state. Call at the start of each request."""
+    _state.broadcasting = None
+    _state.broadcast_action = None
+
+
+def set_broadcasting(value: Optional[bool]) -> None:
+    _state.broadcasting = value
+
+
+def get_broadcasting() -> Optional[bool]:
+    return getattr(_state, "broadcasting", None)
+
+
+def request_broadcast(action: str) -> None:
+    """Record a broadcast directive. ``action`` is "start" or "stop"."""
+    _state.broadcast_action = action
+
+
+def get_broadcast_action() -> Optional[str]:
+    return getattr(_state, "broadcast_action", None)