backend: per-conversation unread counts

Count messages from others newer than the caller's read pointer alongside the
existing last-message lookup, expose it as unreadCount on
ConversationSummary, and derive the unread boolean from it.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

backend/src/types/messaging.ts

@@ -21,5 +21,7 @@ export type ConversationSummary = {
   participants: Participant[];
   lastMessage: ConversationMessage | null;
   unread: boolean;
+  // Messages from others newer than the caller's read pointer.
+  unreadCount: number;
   updatedAt: string;
 };