Feature request: allow queuing follow-up messages while response is streaming

[voodoo]

Is your feature request related to a problem?
After sending a message, the chat input locks up until the current response finishes streaming. If I think of a follow-up or clarification mid-response, I can't type it — I have to wait and risk forgetting it.

Describe the solution you'd like
A message queue that lets me type and submit follow-up messages while a response is still streaming. They'd be sent in order after the current response finishes, or ideally the AI could see the queued messages and adjust its response on the fly.

Describe alternatives you've considered

• Just waiting (lose the thought)
• Typing in a separate editor and pasting later (clunky)
• Using a different app that supports this (some do)

Additional context
PR #3317 added a run-queue with steer/followup/collect modes on the backend but the frontend UI for it isn't shipped yet. This issue is requesting that frontend UI.

[hgunduzoglu]

Taking this one. The backend run-queue from #3317 (steer/followup/collect modes) is already in place, so this is about shipping the frontend: keep the chat composer usable while a response is streaming, queue submitted follow-ups, and send them in order once the current turn finishes. I'll start by mapping the existing queue surface onto the composer's streaming-lock.