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 -->

packages/frontend/admin/package.json

@@ -69,7 +69,7 @@
     "tailwind-merge": "^3.4.0",
     "tailwindcss": "^4.1.17",
     "tailwindcss-animate": "^1.0.7",
-    "vitest": "^3.2.4"
+    "vitest": "^4.0.18"
   },
   "scripts": {
     "build": "affine bundle",

packages/frontend/admin/tsconfig.json

@@ -2,6 +2,7 @@
   "extends": "../../../tsconfig.web.json",
   "include": ["./src", "./src/config.json"],
   "compilerOptions": {
+    "types": ["build-config", "affine__env", "node"],
     "resolveJsonModule": true,
     "rootDir": "./src",
     "outDir": "./dist",