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/src/db/schema/messaging.ts

@@ -0,0 +1,71 @@
+import {
+  boolean,
+  index,
+  pgTable,
+  text,
+  timestamp,
+  uniqueIndex,
+  uuid,
+} from "drizzle-orm/pg-core";
+
+import { organization, user } from "./auth.js";
+
+// A conversation between clinic staff, scoped to a clinic (organization). `name`
+// is set for named/group conversations; a 1:1 DM leaves it null and the display
+// name is derived from the other participant.
+export const conversations = pgTable(
+  "conversations",
+  {
+    id: uuid("id").primaryKey().defaultRandom(),
+    organizationId: text("organization_id")
+      .notNull()
+      .references(() => organization.id, { onDelete: "cascade" }),
+    name: text("name"),
+    isGroup: boolean("is_group").notNull().default(false),
+    createdBy: text("created_by").references(() => user.id, {
+      onDelete: "set null",
+    }),
+    createdAt: timestamp("created_at").defaultNow().notNull(),
+    // Bumped on each new message so the inbox can sort by recency.
+    updatedAt: timestamp("updated_at")
+      .defaultNow()
+      .$onUpdate(() => new Date())
+      .notNull(),
+  },
+  (t) => [index("conversations_org_idx").on(t.organizationId)],
+);
+
+export const conversationParticipants = pgTable(
+  "conversation_participants",
+  {
+    id: uuid("id").primaryKey().defaultRandom(),
+    conversationId: uuid("conversation_id")
+      .notNull()
+      .references(() => conversations.id, { onDelete: "cascade" }),
+    userId: text("user_id")
+      .notNull()
+      .references(() => user.id, { onDelete: "cascade" }),
+    // Last time this participant read the conversation; drives unread state.
+    lastReadAt: timestamp("last_read_at"),
+  },
+  (t) => [
+    uniqueIndex("conv_participant_uidx").on(t.conversationId, t.userId),
+    index("conv_participant_user_idx").on(t.userId),
+  ],
+);
+
+export const messages = pgTable(
+  "messages",
+  {
+    id: uuid("id").primaryKey().defaultRandom(),
+    conversationId: uuid("conversation_id")
+      .notNull()
+      .references(() => conversations.id, { onDelete: "cascade" }),
+    senderId: text("sender_id")
+      .notNull()
+      .references(() => user.id, { onDelete: "cascade" }),
+    body: text("body").notNull(),
+    createdAt: timestamp("created_at").defaultNow().notNull(),
+  },
+  (t) => [index("messages_conv_idx").on(t.conversationId, t.createdAt)],
+);