[BUG] User questions and answers lost from transcript while background subagents are running

Description

When background subagents (Task agents with run_in_background: true) are running, if the user types a question in the main Claude Code interface, both the question and the response are silently lost. They do not appear in the visible conversation, and they are also not visible when viewing the transcript via Ctrl+O.

Steps to Reproduce

1. Start a Claude Code session
2. Launch one or more background subagents (e.g., via the Task tool with run_in_background: true)
3. While the subagents are running, type a question in the main input
4. Observe that the question appears to be processed, but neither the question nor the answer is visible in the conversation
5. Press Ctrl+O to view the full transcript — the question and answer are missing there as well

Expected Behavior

• User questions typed while background subagents are running should be visible in the main conversation
• The responses to those questions should also be visible
• Both should appear in the transcript (Ctrl+O) for later review

Actual Behavior

• The question and answer are silently swallowed
• They do not appear in the conversation view
• They do not appear in the Ctrl+O transcript view
• There is no indication to the user that their input was lost

Impact

This makes it impossible to ask lightweight questions (e.g., clarifications, unrelated queries) while background agents are doing work, without interrupting/cancelling all running subagents first.

Related Issues

• #22844 — User messages disappear while Claude is thinking (similar symptom, different trigger)
• #17011 — Background Task agents silently lose all output
• #5817 — User input is ignored and "Previous query still processing"

Environment

• Claude Code CLI
• macOS (Darwin 25.2.0)