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/framework/std/vitest.config.ts

@@ -1,3 +1,4 @@
+import { playwright } from '@vitest/browser-playwright';
 import { defineConfig } from 'vitest/config';
 
 export default defineConfig({
@@ -8,15 +9,14 @@ export default defineConfig({
     browser: {
       enabled: true,
       headless: true,
-      name: 'chromium',
-      provider: 'playwright',
+      instances: [{ browser: 'chromium' }],
+      provider: playwright(),
       isolate: false,
-      providerOptions: {},
     },
     include: ['src/__tests__/**/*.unit.spec.ts'],
     testTimeout: 500,
     coverage: {
-      provider: 'istanbul', // or 'c8'
+      provider: 'istanbul',
       reporter: ['lcov'],
       reportsDirectory: '../../../.coverage/std',
     },