Commit 87a0886 (#400) introduced a promptReplayed flag to distinguish background task results from the current prompt's result. The flag starts false and only becomes true when the user message is replayed through the query stream with a matching UUID.

In practice, Claude Code either doesn't replay the user message or replays it with a different UUID. This causes promptReplayed to stay false for every prompt, so the result is always discarded as a "background task result". The while(true) loop then blocks forever waiting for a result that will never come — hanging every prompt indefinitely.

Wire logs from two independent sessions confirm:

1. session/prompt request is sent
2. Notifications flow normally (stream events, tool calls, agent messages)
3. stderr shows "consuming background task result" — the result is discarded
4. No response to the session/prompt request is ever sent
5. The client hangs forever (no timeout mechanism)

Fix

Replace promptReplayed with backgroundInitPending — a flag that detects the actual fingerprint of a background task completion: a system init message immediately followed by a result with no intervening stream_event or assistant messages.

This works because:

• Background tasks produce init → result with nothing in between
• Our prompt's processing produces init → stream_events → result (Claude always streams its response before the result)
• The stream_event / assistant messages clear backgroundInitPending, so our result is accepted

This approach doesn't depend on user message replay at all, making it robust regardless of whether replay-user-messages is working correctly in the SDK.

Tests added (7 new)

• Result accepted when no user message replay arrives (the core regression)
• Result accepted when init + stream events precede result without replay
• init → result (no activity) correctly consumed as background task, followed by our result with stream events
• Result accepted when stream events precede result without replay
• Background task consumed when replay IS present (preserves original Don't get out of sync when background task creates new init/result (try 2) #400 intent)
• Result accepted when replay has mismatched UUID
• Existing background task test continues to pass
• Manual burn-in verification