Should Codex own the project state, or should the workspace sit above Codex?

I’ve been thinking about where project state should actually live. If Codex owns it, everything stays tied to one agent. But if the workspace sits above the agent, you can switch between Codex, Claude, or other tools without losing the project context. The second approach makes more sense to me, but I’m curious what others think. Where would you put the shared state?