Same bug as MissionInterviewModal: handleSubmitResponse was calling the
API without first reconnecting to the SSE stream. The stream's complete
event closes the connection after each question delivery, so after the
user submits an answer, a fresh connection is needed to receive the
next question or summary.
Also cleans up the stream on API error, matching MissionInterviewModal.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>