Add Playwright configuration and initial tests for landing page

- Created playwright.config.ts for test configuration
- Added .last-run.json to store test run status
- Implemented landing.test.ts with tests for navbar visibility and navigation
- Removed unused server proxy configuration from vite.config.ts

test-results/.last-run.json

@@ -0,0 +1,4 @@
+{
+  "status": "passed",
+  "failedTests": []
+}