Draft: Update `SyncStore` with changes to the `SyncEngine` state

[MatthewTighe]

Pull Request checklist

• [ ] Quality: This PR builds and passes detekt/ktlint checks (A pre-push hook is recommended)
• [ ] Tests: This PR includes thorough tests or an explanation of why it does not
• [ ] Changelog: This PR includes a changelog entry or does not need one
• [ ] Accessibility: The code in this PR follows accessibility best practices or does not include any user facing features

After merge

• Milestone: Make sure issues closed by this pull request are added to the milestone of the version currently in development.
• Breaking Changes: If this is a breaking change, please push a draft PR on Reference Browser to address the breaking issues.

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