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 -->

package.json

@@ -64,9 +64,9 @@
     "@types/node": "^22.0.0",
     "@typescript-eslint/parser": "^8.55.0",
     "@vanilla-extract/vite-plugin": "^5.0.0",
-    "@vitest/browser": "^3.2.4",
-    "@vitest/coverage-istanbul": "^3.2.4",
-    "@vitest/ui": "^3.2.4",
+    "@vitest/browser": "^4.0.18",
+    "@vitest/coverage-istanbul": "^4.0.18",
+    "@vitest/ui": "^4.0.18",
     "cross-env": "^10.1.0",
     "electron": "^39.0.0",
     "eslint": "^9.39.2",
@@ -90,7 +90,7 @@
     "typescript-eslint": "^8.55.0",
     "unplugin-swc": "^1.5.9",
     "vite": "^7.2.7",
-    "vitest": "^3.2.4"
+    "vitest": "^4.0.18"
   },
   "packageManager": "yarn@4.12.0",
   "resolutions": {