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

playwright.config.ts

@@ -0,0 +1,18 @@
+import type { PlaywrightTestConfig } from "@playwright/test";
+
+const config: PlaywrightTestConfig = {
+  testDir: "./tests",
+  webServer: {
+    command: "npm run dev",
+    port: 5173,
+    timeout: 120000,
+  },
+  use: {
+    trace: "on-first-retry",
+    headless: false,
+    viewport: { width: 1280, height: 800 },
+  },
+  reporter: [["html", { output: "test-results" }]],
+};
+
+export default config;