Auto-spawn parallel session when input is typed while Claude is processing

When Claude Code is mid-response or thinking, new user input is queued and processed sequentially. It would be useful if Claude Code could detect that new input is unrelated to the current task and automatically open a parallel session to handle it concurrently, rather than blocking until the current turn completes.

Use case: User asks Claude to do a long task, then thinks of something unrelated they want to ask/do — instead of waiting, a new session spins up automatically.