Sticky task summary header + tab title status per agent/terminal

What feature would you like to see?

Problem
When working with multiple Codex agents/terminals in parallel, it's easy to forget each tab’s current task. This causes misdirected messages and context loss.

Proposed solution
• Add a persistent sticky header at the top of each agent/terminal showing:
– One-sentence task summary (editable)
– Repo/workspace, branch, cwd
– Small status chip (idle/running + elapsed)
• Reflect the summary in the tab title (truncated) for quick identification.
• Provide fast controls: pencil icon in the header and a /summary command.
• Expose a minimal API so extensions/tools can set/update the summary programmatically.
• Persist per agent/session and across reloads; ensure good a11y semantics.

Why this matters
Reduces errors when multitasking, speeds task switching, and improves clarity without turning Codex into a project manager.

Non-goals
Not a full PM overlay—just lightweight, always-visible context.

Are you interested in implementing this feature?

Yes—happy to help with design/spec and testing; can attempt a PR with guidance to the relevant components.

Additional information

Related: #4607 requests a similar sticky header. This proposal adds tab-title mirroring, quick edit/command, and a small API for programmatic updates.