web(realtime): refresh chat info panel on chat updates

web/src/hooks/useRealtime.ts

@@ -133,6 +133,7 @@ export function useRealtime() {
         if (event.event === "chat_updated") {
           const chatId = Number(event.payload.chat_id);
           if (Number.isFinite(chatId)) {
+            window.dispatchEvent(new CustomEvent("bm:chat-updated", { detail: { chatId } }));
             scheduleReloadChats();
             if (chatStore.activeChatId === chatId || (chatStore.messagesByChat[chatId]?.length ?? 0) > 0) {
               void chatStore.loadMessages(chatId);