docs(test-parallel): add guidance on shared state in parallel tests

[yury-s]

Summary

• Add an "Avoiding shared state in parallel tests" section to the parallelism guide: explains Playwright's built-in isolation (separate worker processes, isolated browser contexts) and the genuine pitfalls (external resources, files on disk, worker-shared state).

Fixes #41671

[github-actions]

Test results for "MCP"

2 failed
❌ [msedge] › mcp/annotate.spec.ts:497 › should disengage annotate mode when --annotate client disconnects @mcp-windows-latest-msedge
❌ [webkit] › mcp/cli-killall.spec.ts:42 › kill-all kills filtered dashboard pid @mcp-ubuntu-latest-webkit

7758 passed, 1249 skipped

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Merge workflow run.

[github-actions]

Test results for "tests 1"

7 flaky

⚠️ [chromium-library] › library/inspector/recorder-api.spec.ts:120 › should type `@frozen-time-library-chromium-linux`
⚠️ [chromium-library] › library/video.spec.ts:717 › screencast › should work with video+trace `@chromium-ubuntu-22.04-arm-node20`
⚠️ [chromium-library] › library/popup.spec.ts:260 › should not throw when click closes popup `@chromium-ubuntu-22.04-node24`
⚠️ [chromium-library] › library/video.spec.ts:337 › screencast › should work for popups `@chromium-ubuntu-22.04-node24`
⚠️ [chromium-library] › library/tracing.spec.ts:429 › should produce screencast frames crop `@chromium-ubuntu-22.04-node20`
⚠️ [chromium-library] › library/video.spec.ts:275 › screencast › should capture navigation `@chromium-ubuntu-22.04-node20`
⚠️ [chromium-library] › library/video.spec.ts:717 › screencast › should work with video+trace `@chromium-ubuntu-22.04-node20`

49517 passed, 1161 skipped

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Merge workflow run.

[dgozman]

I am not sure this helps much as it's written. A wall of text that nobody will read. If it were to have some snippets/recipes to deal with common parallel-specific issues, that would probably be better.

[yury-s]

Good call — reworked it into short recipes with snippets instead of prose (4f0a95320), one per common parallel-specific issue:

• give each test its own backend data via testInfo.testId
• write to testInfo.outputPath() for unique file paths
• a ❌/✅ pair for not leaking test state through module-level variables

Intro is down to one sentence.