Cross-device continuity for Codex tasks

What variant of Codex are you using?

Mac Client

What feature would you like to see?

I use the same GitLab project on two computers. Code can be synchronized through Git, but Codex task context cannot be reliably continued across devices. Discussions, architectural decisions, and implementation plans created at work are unavailable when I continue on my home computer.
It would be helpful if Codex could:
Sync tasks across devices under the same account.
Allow an existing task to be reopened and rebound to the same repository on another computer.
Preserve conversation context while clearly detecting differences in local repository state.
Optionally provide a project-level shared context across tasks.
This is different from syncing code through Git; the missing part is continuity of the Codex conversation and project decisions.

Additional information

_No response_