Hey! Thanks for the detailed report. What you’re describing is actually the current expected behavior for queued messages: they’re held until the agent’s current turn finishes, then dispatched automatically. This applies to all models, including Codex.
The closest existing mechanism for what you want is Cmd+Enter (or Ctrl+Enter on Windows/Linux), which sends your message immediately and the agent considers it right away alongside its current work. You can read more about it in the Agent docs under “Immediate messaging”.
That said, what you’re describing (the agent picking up queued messages mid-turn, between tool calls, without stopping) is a step beyond what the current queue or immediate-send provides. A few others have requested similar behavior: