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

web/src/components/ChatList.tsx

@@ -135,9 +135,15 @@ export function ChatList() {
               <div className="min-w-0 flex-1">
                 <div className="flex items-center justify-between gap-2">
                   <p className="truncate text-sm font-semibold">{chatLabel(chat)}</p>
-                  <span className="shrink-0 text-[11px] text-slate-400">
-                    {messagesByChat[chat.id]?.length ? "now" : ""}
-                  </span>
+                  {(chat.unread_count ?? 0) > 0 ? (
+                    <span className="inline-flex min-w-5 items-center justify-center rounded-full bg-sky-500 px-1.5 py-0.5 text-[10px] font-semibold text-slate-950">
+                      {chat.unread_count}
+                    </span>
+                  ) : (
+                    <span className="shrink-0 text-[11px] text-slate-400">
+                      {messagesByChat[chat.id]?.length ? "now" : ""}
+                    </span>
+                  )}
                 </div>
                 <p className="truncate text-xs text-slate-400">{chat.type}</p>
               </div>