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/package.json

@@ -6,7 +6,7 @@
     "dev": "vite",
     "build": "tsc",
     "test:unit": "vitest --browser.headless --run",
-    "test:debug": "PWDEBUG=1 npx vitest"
+    "test:debug": "PWDEBUG=1 npx vitest --browser.headless=false"
   },
   "sideEffects": false,
   "keywords": [],
@@ -41,10 +41,11 @@
   ],
   "devDependencies": {
     "@vanilla-extract/vite-plugin": "^5.0.0",
+    "@vitest/browser-playwright": "^4.0.18",
     "vite": "^7.2.7",
     "vite-plugin-istanbul": "^7.2.1",
     "vite-plugin-wasm": "^3.5.0",
-    "vitest": "^3.2.4"
+    "vitest": "^4.0.18"
   },
   "version": "0.26.3"
 }