feat(analytics): wire flow usage tracking into session matching and resolution

- In `start_session`: increment `flow.usage_count` and set `flow.last_matched_at`
  when a flow is matched to a new session; errors are caught without blocking
- In `resolve_session`: recalculate `flow.success_rate` as (resolved / total)
  across all sessions ever matched to the flow after each resolution; errors
  are caught without blocking the session close

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/services/flowpilot_engine.py

@@ -11,7 +11,7 @@ from datetime import datetime, timezone
 from typing import Any, Optional
 from uuid import UUID
 
-from sqlalchemy import select, or_
+from sqlalchemy import select, func, or_
 from sqlalchemy.ext.asyncio import AsyncSession
 from sqlalchemy.orm import selectinload
 
@@ -20,6 +20,7 @@ from app.core.config import settings
 from app.services.notification_service import notify
 from app.models.ai_session import AISession
 from app.models.ai_session_step import AISessionStep
+from app.models.tree import Tree
 from app.schemas.ai_session import (
     AISessionCreateRequest,
     AISessionCreateResponse,
@@ -308,6 +309,16 @@ async def start_session(
     )
     db.add(session)
 
+    # 7a. Update matched flow usage tracking
+    if matched_flow_id:
+        try:
+            flow_result = await db.get(Tree, matched_flow_id)
+            if flow_result:
+                flow_result.usage_count = (flow_result.usage_count or 0) + 1
+                flow_result.last_matched_at = datetime.now(timezone.utc)
+        except Exception as e:
+            logger.warning("Failed to update flow usage stats for flow %s: %s", matched_flow_id, e)
+
     # 7. Create first step
     step = _create_step_from_parsed(
         session_id=session.id,
@@ -457,6 +468,28 @@ async def resolve_session(
     # Queue for Knowledge Flywheel analysis
     session.analysis_status = "pending"
 
+    # Recalculate success_rate for the matched flow
+    if session.matched_flow_id:
+        try:
+            flow = await db.get(Tree, session.matched_flow_id)
+            if flow:
+                total_result = await db.execute(
+                    select(func.count(AISession.id))
+                    .where(AISession.matched_flow_id == flow.id)
+                )
+                resolved_result = await db.execute(
+                    select(func.count(AISession.id))
+                    .where(
+                        AISession.matched_flow_id == flow.id,
+                        AISession.status == "resolved",
+                    )
+                )
+                total = total_result.scalar() or 0
+                resolved_count = resolved_result.scalar() or 0
+                flow.success_rate = round(resolved_count / total, 3) if total else None
+        except Exception as e:
+            logger.warning("Failed to recalculate success_rate for flow %s: %s", session.matched_flow_id, e)
+
     await db.flush()
 
     # Push documentation to PSA if ticket is linked