Revert "chore: tidy up headless-shell hacks (#33967)"

[mxschmitt]

This reverts commit 38758c0.

#34636
#34508

[github-actions]

Test results for "tests 1"

1 failed
❌ [webkit-page] › tests/page/page-leaks.spec.ts:82:5 › click should not leak @webkit-ubuntu-22.04-node18

12 flaky

⚠️ [firefox-library] › tests/library/role-utils.spec.ts:442:5 › svg role=presentation @firefox-ubuntu-22.04-node18
⚠️ [firefox-page] › tests/page/page-evaluate.spec.ts:403:3 › should throw for too deep reference chain @firefox-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/browsercontext-clearcookies.spec.ts:92:3 › should remove cookies by domain @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/browsercontext-har.spec.ts:455:3 › should update har.zip for page @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/proxy.spec.ts:93:11 › should proxy local network requests › with other bypasses › link-local @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/trace-viewer.spec.ts:109:1 › should show tracing.group in the action list with location @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/trace-viewer.spec.ts:966:1 › should show action source @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/trace-viewer.spec.ts:1611:1 › canvas clipping @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › tests/library/tracing.spec.ts:545:5 › should export trace concurrently to second navigation @webkit-ubuntu-22.04-node18
⚠️ [webkit-page] › tests/page/page-leaks.spec.ts:107:5 › fill should not leak @webkit-ubuntu-22.04-node18
⚠️ [webkit-page] › tests/page/page-leaks.spec.ts:161:5 › waitFor should not leak @webkit-ubuntu-22.04-node18
⚠️ [playwright-test] › tests/ui-mode-test-watch.spec.ts:145:5 › should watch all @windows-latest-node18-1

37798 passed, 655 skipped
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Merge workflow run.