Two separate things are happening here:
1) The Anthropic cooldown (rate_limit)
That one you generally don’t want to “turn off”. It’s OpenClaw’s backoff/circuit-breaker after Anthropic returns 429s. If you forcibly bypass it, you’ll usually just keep hammering Anthropic and get more 429s (and longer backoffs).
Best fix is: wait out the cooldown or add a fallback to a different provider (so you still get replies while Anthropic is cooling down).
2) The "[Queued messages while agent was busy]" wrapper
This is configurable. It happens when your queue mode is collect (default), and multiple inbound messages arrive while a run is in-flight, so OpenClaw coalesces them into one follow-up prompt.
If you want to avoid that wrapper, switch queue mode away from collect:
Quick (per-session, from chat)
Send as a standalone message:
/queue followup → process each message separately (no “Queued …” bundle)
/queue steer → inject new messages into the current run
/queue interrupt → abort the current run and run the newest message