Feature request: queue messages instead of interrupting current response

Problem

When typing a second message while Claude Code is still processing the first one, the current response gets interrupted. There's no way to queue a follow-up message to run after the current one completes.

Desired behavior

Add a mode where new messages are queued and processed sequentially after the current response finishes, rather than interrupting it. The user should still be able to explicitly cancel with Ctrl+C if needed.

Use case

Often I think of a follow-up question or next task while Claude is mid-response. I'd like to type it immediately so I don't forget, but without interrupting the work in progress.