A prompt sent while a turn was in flight got rejected with 4009 "session busy",
which pushed clients (the desktop app) into a deadline-bounded busy-retry. When
turn teardown outlived that deadline — e.g. the user hits stop while a slow,
non-interruptible tool (web_search, read_file, an MCP call) is mid-flight, since
the sequential executor only checks the interrupt flag between tools — the
resubmitted message was silently dropped: "it just doesn't listen".
Wire the previously-dead display.busy_input_mode config into prompt.submit:
instead of rejecting, apply the policy and queue the message to run as the next
turn (drained in run()'s tail, ahead of goal/notification follow-ups). Modes:
interrupt (default) interrupts the live turn so it winds down promptly then runs
the queued message; queue runs it after the current turn finishes; steer injects
it into the live turn when accepted, else queues. The queued slot pins the
sender's transport and losslessly merges a second arrival. No client deadline,
no dropped sends.
