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>

backend/drizzle/meta/_journal.json

@@ -43,6 +43,13 @@
       "when": 1780850717058,
       "tag": "0005_true_gwen_stacy",
       "breakpoints": true
+    },
+    {
+      "idx": 6,
+      "version": "7",
+      "when": 1780856647280,
+      "tag": "0006_square_wither",
+      "breakpoints": true
     }
   ]
 }