live: AMI-fed live state, /api/live WebSocket, dashboard and status dots

LiveState loads extension states and registered devices from Asterisk on
every AMI connect and follows ExtensionStatus/ContactStatus; the hub sends
a snapshot then deltas batched every 250 ms (devices for admins only),
pings every 30 s and closes unauthenticated sockets with 4401. The web UI
keeps one reconnecting socket in a zustand store, shows a Reconnecting
banner, a Dashboard (online, on a call, telephony engine) and status dots.

Fix: Asterisk 24 has no 'pjsip reload'; reload with
'module reload res_pjsip.so'. AMI errors now carry the CLI output.

Milestone check, automated: call-test.ts registers two baresip phones and
holds a 30 s call with RTP both ways (pnpm test:asterisk); the recorded
session drives the live-state tests. scripts/e2e/m2-live.mjs runs api +
Asterisk + phones + browser on a private Docker network: a new extension
is live in Asterisk in ~1.3 s, the dashboard shows 2/2 online and red dots
during the call.

Task: M2-T6

apps/api/package.json

@@ -13,6 +13,7 @@
   "dependencies": {
     "@fastify/cookie": "^11.1.3",
     "@fastify/static": "^10.1.6",
+    "@fastify/websocket": "^11.3.4",
     "@node-rs/argon2": "^2.2.2",
     "@selfphoneng/shared": "workspace:*",
     "drizzle-orm": "^0.45.4",
@@ -22,6 +23,7 @@
   },
   "devDependencies": {
     "@types/pg": "^8.23.1",
+    "@types/ws": "^8.18.2",
     "drizzle-kit": "^0.31.11"
   }
 }