Allow Codex to ingest queued corrections while the current turn is still running

What feature would you like to see?

Summary

Codex should notice new user messages while it's still mid-turn so it can adjust course before wrapping up.

Problem statement

1. Kick off a long-running Codex turn (e.g. running a gnarly test suite).
2. Realize you forgot an important detail or need to tweak the ask.
3. Today you can send another message, but it just sits in the queue until the agent fully finishes, so no mid-flight fix happens. PR #2637 gave us the queue, but the agent reads it only after the turn.

Prior work

• #2011 asked for typing the next prompt while Codex is busy, and #2102 adds the overlay so we can actually do that.
• PR #2637 merged the queue plumbing, but delivery waits until the previous turn ends.

Proposal

Let the agent peek at the queued messages while it's still working. When the user hits Enter, Codex should be able to:

• Interleave the new instructions the next time it loops on tools/reasoning (maybe behind a config gate).
• Decide whether to stop the current plan, adjust, or acknowledge and carry on.

Acceptance criteria

• Sending a follow-up while Codex shows "Working..." results in the agent responding to the update before the original turn finishes.
• If the agent cannot safely merge the new message, it tells the user and keeps the message queued for later.
• Telemetry/logging exists so we can see how often mid-turn updates happen (useful for safety watchdogs).

Additional context

This unlocks fast "oops, I meant file X not file Y" corrections without waiting minutes for a big run to finish. Right now we kinda sit on our hands until the prior turn ends.

Are you interested in implementing this feature?

_No response_

Additional information

_No response_