[BUG] Remote Control: message typed while agent is busy is lost when switching chats (un-sent draft discarded, no queue)

Bug Report

Summary

In Remote Control (mobile / claude.ai → CLI), a message I type while the agent is busy stays in the compose box as an un-sent draft (there is no queue-while-busy), and that draft is silently discarded when I switch to another chat/session and come back. The input is lost — never delivered to the agent, never recoverable.

Steps to Reproduce

1. Connect a session via Remote Control and open it from the mobile app / web.
2. Send a prompt so the agent starts a long-running turn (it is "busy").
3. While it is still working, type a follow-up message in the input box. (It does not send/queue — it just sits as a draft, since there is no queue mode.)
4. Without sending, switch to a different chat/session in the app.
5. Switch back to the original session.

Expected Behavior

The drafted (un-sent) message should still be in the input box — or, better, it should have been queued and delivered when the turn finished. Either way it must not be silently lost.

Actual Behavior

The drafted message is gone. It was never delivered to the agent and is not recoverable. Switching chats while the agent is busy = data loss of whatever I was composing.

Why this is more than ergonomics

On desktop you can wait and the box keeps your text. On mobile Remote Control the natural workflow is to compose the next instruction while watching the busy turn, then glance at another session. That exact normal flow throws the message away. Combined with the absence of a queue-while-busy mode, there is no safe way to capture a follow-up during an active turn from mobile.

Suggested Fixes (either/both)

1. Persist the per-session draft across chat/session switches in the Remote Control UI (don't clear the compose box on navigate-away).
2. Queue-while-busy delivery (see #50246 / #62856 / #63190): allow the message to be queued and auto-delivered when the current turn ends, rather than leaving it as a discardable draft.

Related

• #50246 (Message queue mode) — I commented there with this mobile variant
• #62856 (Compose-while-working with send-time interrupt/queue choice)
• #63190 (Deferred Messages)
• Distinct from #42671 / #62513 (phone→CLI delivery): here the message is never even sent — it's a draft lost on local navigation.

Environment

• Remote Control from mobile / claude.ai web
• CLI version: 2.1.160