feat(har): use engine timestamps instead of server Date

[dcrousso]

whether it be from a dedicated protocol timestamp or the more general timing , we should use a value from the engine for startDateTime instead of the playwright server Date

[github-actions]

Test results for "MCP"

1 failed
❌ [chrome] › mcp/launch.spec.ts:64 › persistent context @mcp-ubuntu-latest-chrome

7229 passed, 1103 skipped

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Merge workflow run.

[github-actions]

Test results for "tests 1"

6 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:682 › screencast › should capture full viewport on hidpi `@chromium-ubuntu-22.04-arm-node20`
⚠️ [chromium-library] › library/video.spec.ts:337 › screencast › should work for popups `@chromium-ubuntu-22.04-node20`
⚠️ [chromium-library] › library/beforeunload.spec.ts:130 › should support dismissing the dialog multiple times `@chromium-ubuntu-22.04-node22`
⚠️ [firefox-library] › library/har-websocket.spec.ts:170 › should record websocket connection failure `@firefox-ubuntu-22.04-node20`
⚠️ [playwright-test] › ui-mode-trace.spec.ts:704 › should indicate current test status `@windows-latest-node20`

39459 passed, 775 skipped

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Merge workflow run.