GitHub doesn't natively support complex synchronization scenarios as you've described without some automation. If advanced synchronization and project management features are critical for your workflow, it might be worth investing time in automation or integrating more feature-rich third-party tools. ZenHub and Jira are great examples of this.

If you would like to attempt some level of synchronicity, here are a few options:

• If your major project is meant to track work from different repositories, you can manually add issues or pull requests from different repositories into one project board. As long as the board is at the organization level, you can pull in tasks from any repository within the organization.
• For shared issues, create the issue in one repository, and then manually add the issue as a linked card in the project of another repository. You would then have to track changes on the original issue and manually mirror those changes on the other repository's project board.
• You can create notes in your project board that link back to issues in other repositories. This allows you to keep a reference to tasks in other repositories. However, these aren't dynamic – meaning that any changes to the status of the linked issue won't be automatically reflected in the note.
• Whenever there are shared issues or tasks, cross-reference them by commenting in each issue with the link to the other. This creates a traceable link between the two. While it doesn’t solve the synchronization problem, it helps in tracking and ensuring that one doesn’t get lost while navigating complex project dependencies.
• Labeling can help in identifying the shared and non-shared issues. You could establish a consistent labeling system that's used across repositories. When you want to synchronize or check shared issues, you can then filter by those labels.

Good luck!

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Example Github project - Arch as code
We create the Github issues on 6 repositories, belonging to multiple products/projects having different squads.

All the issues appear on one single Project board for tracking and management purpose. We've linked this project on all 6 repos and so the issues are in sync between the project and the repo.

We've manually added the issues to Epics (issues which we differentiate by adding a label as epic) for high level categorization and roadmap view.