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/app/_components/core/index.ts

@@ -3,6 +3,7 @@
  */
 
 export * from "./auth-back-button";
+export * from "./bottom-sheet";
 export * from "./dialog";
 export * from "./loading-indicator";
 export * from "./mobile-shell";