"""WebSocket server, connection registry, and frame routing.

Runs on the gateway's asyncio loop (started in ``AndroidAdapter.connect()``).
Uses the ``websockets`` core dep (v15): ``websockets.serve(handler, host,
port, ssl=ctx)``.

Per-connection handler:
  1. Await first frame; must be ``hello {token, device_id, device_name,
     caps, fcm_token?}``. Verify token (constant-time) + allowlist. On
     failure: send ``error {code:"auth"}`` and close.
  2. On success: register in the connection registry (``device_id ->
     {ws, caps, fcm_token}``), send ``hello.ack {server_caps, sync_cursor,
     channels[]}``.
  3. Loop: decode frames, dispatch to adapter inbound handlers.
  4. On close: deregister; if no devices remain, ensure pending outbox
     frames have push fired.

Routing: ``emit(chat_id, frame)`` broadcasts to ALL connected devices
(single-user model). Heartbeat via WS ping/pong + app-level ping/pong.
Backpressure: bounded per-connection send queue; coalesce ``message.update``
under pressure, never drop ``message``/``tool.end``/``notification``.

Milestone M1.
"""