Support Multi-Chat in Codex harness

[sandy081]

Summary

Add Multi-Chat support to the Codex harness so it matches the Copilot experience.

Background

• The Multi-Chat feature (previously called Sub-Sessions) is currently available for the Copilot harness and works in AHP sessions for Copilot.
• Team feedback and user studies have shown confusion around the feature and its name; the UX should be consistent across harnesses rather than Copilot-only.
• Codex AHP sessions do not currently show the Multi-Chat UI.

Proposal

• Implement Multi-Chat in the Codex harness with parity to the Copilot implementation and UX.
• Ensure Multi-Chat is available in AHP sessions for Codex as it is for Copilot.
• Minimize agent integration effort (sessions should be transparent to agents where possible), and document any agent-facing changes required.
• Update tests, e2e scenarios, and relevant documentation to reflect Multi-Chat availability in the Codex harness.

Acceptance criteria

• Multi-Chat UI appears and behaves the same in the Codex harness as it does in Copilot.
• Multi-Chat is available and functional in AHP sessions for Codex.
• Agent/handler code for Codex either requires no changes or any required changes are documented and minimal.
• Relevant tests and documentation updated.

Implementation notes

• Verify whether sessions need to be linked or if the agent surface can remain unchanged (transparent sessions).
• Coordinate UX changes with the Copilot harness team to ensure consistency and avoid repeating prior confusion around naming/behavior.
• Add testing steps to validate in manual and automated tests across the Codex harness and AHP sessions.

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Split from #322776 (Claude). This issue tracks the Codex harness.

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