chore: migrate contexts to stores and refresh barrel exports

- Move state management from `src/contexts` to `src/stores` (zustand-based)
- Update barrelsby config to include new stores directory
- Add bottom-sheet and auth-background components
- Auto-open browser on dev server ready in VS Code launch config
- Refresh generated barrel index files

src/integrations/index.ts

@@ -3,6 +3,4 @@
  */
 
 export * from "./browser-detect";
-export * from "../core/net/chat-websocket";
 export * from "./media-recorder";
-export * from "../core/net/message-queue";