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

.vscode/launch.json

@@ -7,7 +7,11 @@
       "request": "launch",
       "runtimeExecutable": "pnpm",
       "runtimeArgs": ["run", "dev"],
-      "console": "integratedTerminal"
+      "serverReadyAction": {
+        "pattern": "- Local:\\s+(https?://\\S+)",
+        "uriFormat": "%s",
+        "action": "openExternally"
+      }
     },
     {
       "name": "Next.js: build",