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 -->

.github/workflows/build-test.yml

@@ -226,7 +226,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        shard: [1, 2]
+        shard: [1, 2, 3, 4, 5]
     steps:
       - uses: actions/checkout@v6
       - name: Setup Node.js
@@ -356,7 +356,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        shard: [1, 2, 3]
+        shard: [1, 2, 3, 4, 5]
     steps:
       - uses: actions/checkout@v6
       - name: Setup Node.js