Why: The final reply is composed after the work loop, and the automatic end check needs its own part and event so the timeline can show it without mixing it into the user-facing text.
Evidence: go test ./...
Impact: New RunPhase finalizing, PartType check, and run.check. Existing payloads are unchanged.
Refs: feature/final-reply-compose
Co-authored-by: Cursor <cursoragent@cursor.com>