fix: bug: architect has no path for approved PRs awaiting initial design questions (#570)

Implementation:
- Added detect_approved_pending_questions() function to identify approved PRs
  that have no ## Design forks section and no Q1:, Q2: comments yet.
- Modified response processing block to handle three session modes:
  1. questions_phase: Resume session for processing Q&A answers
  2. start_questions: Fresh session to post initial design questions
  3. pitch: Original behavior for new pitch generation
- Added build_architect_prompt_for_mode() function to generate appropriate
  prompts for each session mode.
- When an approved PR is detected, the agent posts initial design questions
  (Q1:, Q2:, etc.) and adds the ## Design forks section, transitioning the
  PR into the existing questions phase.

This fixes the issue where approved architect PRs would sit indefinitely
because the agent had no path to start the design conversation.

formulas/run-architect.toml

@@ -169,6 +169,19 @@ description = """
 IMPORTANT: PR creation is handled by bash (architect-run.sh) during the pitch step.
 This step is for documentation only — the actual PR creation happens in research_pitch.
 
+## Approved PR → Initial design questions (issue #570)
+
+When a sprint pitch PR receives an APPROVED review but has no `## Design forks`
+section and no Q1:, Q2: comments yet, the architect enters a new state:
+
+1. detect_approved_pending_questions() identifies this state
+2. A fresh agent session starts with a special prompt
+3. The agent reads the approved pitch, posts initial design questions (Q1:, Q2:, etc.)
+4. The agent adds a `## Design forks` section to the PR body
+5. The PR transitions into the questions phase, where the existing Q&A loop takes over
+
+This ensures approved PRs don't sit indefinitely without design conversation.
+
 Architecture:
 - Bash creates PRs during stateless pitch generation (step 2)
 - Model has no role in PR creation — no Forgejo API access