feat(web-core): implement unread counters and new-messages divider

backend:

- add unread_count to ChatRead serialization

- compute unread_count per chat using message_receipts and hidden messages

web:

- add unread badges in chat list

- track unread boundary per chat in store

- show 'New messages' divider in message list

- update realtime flow to increment/clear unread on incoming events

app/chats/service.py

@@ -26,6 +26,8 @@ async def serialize_chat_for_user(db: AsyncSession, *, user_id: int, chat: Chat)
             if counterpart:
                 display_title = counterpart.name or counterpart.username
 
+    unread_count = await repository.get_unread_count_for_chat(db, chat_id=chat.id, user_id=user_id)
+
     return ChatRead.model_validate(
         {
             "id": chat.id,
@@ -36,6 +38,7 @@ async def serialize_chat_for_user(db: AsyncSession, *, user_id: int, chat: Chat)
             "description": chat.description,
             "is_public": chat.is_public,
             "is_saved": chat.is_saved,
+            "unread_count": unread_count,
             "pinned_message_id": chat.pinned_message_id,
             "created_at": chat.created_at,
         }