chore(infra): add url test to playwright (#11795)

<!-- This is an auto-generated comment: release notes by coderabbit.ai -->
## Summary by CodeRabbit

- **Chores**
  - Updated Playwright test configurations to use full URL strings instead of port numbers for web server identification.
  - Unified server startup approach in test environments by integrating web server configuration directly into Playwright, replacing custom setup scripts.
  - Removed obsolete development server setup files to streamline test initialization.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

tests/affine-local/playwright.config.ts

@@ -18,7 +18,6 @@ const config: PlaywrightTestConfig = {
   fullyParallel: true,
   timeout: process.env.CI ? 50_000 : 30_000,
   outputDir: testResultDir,
-  globalSetup: './dev-server.ts',
   use: {
     baseURL: 'http://localhost:8080/',
     browserName:
@@ -42,6 +41,17 @@ const config: PlaywrightTestConfig = {
   // default 'list' when running locally
   // See https://playwright.dev/docs/test-reporters#github-actions-annotations
   reporter: process.env.CI ? 'github' : 'list',
+  webServer: [
+    {
+      command: 'yarn run -T affine dev -p @affine/web',
+      timeout: 120 * 1000,
+      reuseExistingServer: !process.env.CI,
+      env: {
+        COVERAGE: process.env.COVERAGE || 'false',
+      },
+      url: 'http://localhost:8080',
+    },
+  ],
 };
 
 if (process.env.CI) {