chore(ci): remove client side changes workflow

[pavelfeldman]

Summary

• Removes the pr_check_client_side_changes.yml workflow that auto-filed backport tracking issues in playwright-python/java/dotnet.

[github-actions]

Test results for "tests 1"

3 flaky

⚠️ [chromium-library] › library/video.spec.ts:647 › screencast › should capture full viewport `@chromium-ubuntu-22.04-arm-node20`
⚠️ [chromium-library] › library/video.spec.ts:275 › screencast › should capture navigation `@chromium-ubuntu-22.04-node22`
⚠️ [firefox-library] › library/inspector/cli-codegen-1.spec.ts:1080 › cli codegen › should not throw csp directive violation errors `@firefox-ubuntu-22.04-node20`

41476 passed, 847 skipped

---

Merge workflow run.

[github-actions]

Test results for "MCP"

11 failed
❌ [chrome] › mcp/autowait.spec.ts:19 › racy navigation destroys context @mcp-windows-latest
❌ [chrome] › mcp/cli-core.spec.ts:37 › click button @mcp-windows-latest
❌ [chrome] › mcp/cli-core.spec.ts:51 › click link @mcp-windows-latest
❌ [chrome] › mcp/cli-core.spec.ts:64 › dblclick @mcp-windows-latest
❌ [chrome] › mcp/cli-core.spec.ts:98 › hover @mcp-windows-latest
❌ [chrome] › mcp/dashboard.spec.ts:207 › should enter annotate mode on fresh dashboard.tsx mount with -s --annotate @mcp-windows-latest
❌ [chromium] › mcp/dashboard.spec.ts:207 › should enter annotate mode on fresh dashboard.tsx mount with -s --annotate @mcp-windows-latest
❌ [chromium] › mcp/dashboard.spec.ts:231 › should switch screencast to -s session on show --annotate @mcp-windows-latest
❌ [firefox] › mcp/cli-devtools.spec.ts:204 › video-start-stop @mcp-windows-latest
❌ [firefox] › mcp/cli-devtools.spec.ts:218 › video-chapter @mcp-windows-latest
❌ [webkit] › mcp/dashboard.spec.ts:185 › should start dashboard and annotate when no dashboard is running @mcp-macos-latest

1 flaky

⚠️ [chrome] › mcp/cdp.spec.ts:24 › cdp server `@mcp-windows-latest`

6796 passed, 927 skipped

---

Merge workflow run.

[pavelfeldman]

@copilot resolve the merge conflicts in this pull request