feat: add Playwright configuration and initial e2e test for authentication

- Created Playwright configuration file to set up testing environment.
- Added a new e2e test for user authentication in login.spec.ts.
- Updated tsconfig.node.json to include playwright.config.ts.
- Enhanced vite.config.ts to include API proxying for backend integration.
- Added a placeholder for last run test results in .last-run.json.

frontend/tsconfig.node.json

@@ -14,5 +14,5 @@
     "isolatedModules": true,
     "types": ["node"]
   },
-  "include": ["vite.config.ts"]
+  "include": ["vite.config.ts", "playwright.config.ts"]
 }