fix(ui): compact embedded chat URLs (#2431)

* fix(ui): keep embedded session chat URLs compact

* test(ui): guard embedded session chat URL length

* fix(ui): sync embedded custom themes

Bootstrap custom themes from parent window so iframe URLs stay compact.

Refs #2423

* docs(ui): clarify theme sync precedence

packages/ui/src/components/layout/ContextPanel.tsx

@@ -2457,6 +2457,10 @@ export const ContextPanel: React.FC = () => {
       }
 
       const data = event.data as { type?: unknown };
+      if (data?.type === 'openchamber:theme-sync-request') {
+        postThemeSyncToEmbeddedChat();
+        return;
+      }
       if (data?.type === 'openchamber:chat-settings-request') {
         postChatSettingsSyncToEmbeddedChat();
         return;
@@ -2473,7 +2477,7 @@ export const ContextPanel: React.FC = () => {
 
     window.addEventListener('message', handleMessage);
     return () => window.removeEventListener('message', handleMessage);
-  }, [postChatSettingsSyncToEmbeddedChat, setThemeMode, themeMode]);
+  }, [postChatSettingsSyncToEmbeddedChat, postThemeSyncToEmbeddedChat, setThemeMode, themeMode]);
 
   React.useLayoutEffect(() => {
     const hasAnyChatTab = tabs.some((tab) => tab.mode === 'chat');