SudLogTask reuses ServerLogTask's sample format but only records while
a Sud run is active: starts on Play (fresh start only, not a Pause
resume) and writes logs/log_{date_time}_{sud_name}.log on Stop or
natural completion.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01TvgC7oy9MxaA4ZQxXqkNdS