Refactor auto_triage into smaller focused methods (#63347)

Extract the monolithic auto_triage function body into focused helper
functions: TriageStats, TriageContext, _execute_triage_action,
_prompt_and_execute_flagged_pr, _display_pr_overview_table,
_filter_candidate_prs, _enrich_candidate_details,
_review_workflow_approval_prs, _review_deterministic_flagged_prs,
_review_llm_flagged_prs, _review_passing_prs, and
_display_triage_summary.

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>