Sync status stuck at partial when any non-blocking API call fails

[MethodWhite]

Duplicate of #24540. Closing.

[github-actions]

This issue might be a duplicate of existing issues. Please check:

• Unhandled rejection in background sync leaves TUI stuck in partial status #24540: Describes the same unhandled Promise.all rejection in sync.tsx that leaves the TUI stuck in partial status indefinitely

If you believe this is a distinct issue, please clarify the difference.

[MethodWhite]

Duplicate of #24540. The fix PR #32180 applies to the existing issue.