test: migrate test & utils (#14569)

#### PR Dependency Tree


* **PR #14569** 👈

This tree was auto-generated by
[Charcoal](https://github.com/danerwilliams/charcoal)

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

* **Chores**
* Upgraded development test tooling to Vitest v4 and added Playwright
browser test integration; normalized test configurations and CI shard
matrix.

* **Tests**
* Added a large suite of new integration tests covering editor flows
(edgeless, database, embeds, images, latex, code, clipboard,
multi-editor, presentation, undo/redo, etc.).
* Removed numerous end-to-end Playwright test suites across the same
feature areas.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

blocksuite/integration-test/vitest.config.ts

@@ -1,4 +1,5 @@
 import { vanillaExtractPlugin } from '@vanilla-extract/vite-plugin';
+import { playwright } from '@vitest/browser-playwright';
 import { defineConfig } from 'vitest/config';
 
 export default defineConfig(_configEnv =>
@@ -18,13 +19,13 @@ export default defineConfig(_configEnv =>
       retry: process.env.CI === 'true' ? 3 : 0,
       browser: {
         enabled: true,
-        headless: process.env.CI === 'true',
+        headless: true,
         instances: [
           { browser: 'chromium' },
           { browser: 'firefox' },
           { browser: 'webkit' },
         ],
-        provider: 'playwright',
+        provider: playwright(),
         isolate: false,
         viewport: {
           width: 1024,
@@ -32,16 +33,13 @@ export default defineConfig(_configEnv =>
         },
       },
       coverage: {
-        provider: 'istanbul', // or 'c8'
+        provider: 'istanbul',
         reporter: ['lcov'],
         reportsDirectory: '../../.coverage/integration-test',
       },
       deps: {
         interopDefault: true,
       },
-      testTransformMode: {
-        web: ['src/__tests__/**/*.spec.ts'],
-      },
     },
   })
 );