feat: real-time staff messaging over Socket.io

Add conversations/participants/messages tables, a participant-scoped REST
API (/api/conversations) and a Socket.io server (session-authenticated
handshake; per-user + per-conversation rooms) sharing the HTTP port. New
messages broadcast live and create per-recipient notifications. Also lands
the notifications table + service + routes (used by the message flow). The
Messages page is rewritten: live threads, unread state, and a compose
dialog to start a conversation with a clinic member.

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

frontend/package.json

@@ -45,6 +45,7 @@
     "react-jsx-parser": "^2.4.1",
     "shadcn": "^4.8.3",
     "shiki": "^4.1.0",
+    "socket.io-client": "^4.8.3",
     "streamdown": "^2.5.0",
     "tailwind-merge": "^3.6.0",
     "tokenlens": "^1.3.1",