feat(billing): add BillingService.start_trial; wire into /auth/register

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

backend/app/api/endpoints/auth.py

@@ -195,26 +195,30 @@ async def register(
         # Now set account owner and create subscription
         new_account.owner_id = new_user.id
 
-        # Apply plan/trial from invite code if present
-        sub_plan = "free"
-        sub_status = "active"
-        period_start = None
-        period_end = None
         if invite_code_record and invite_code_record.assigned_plan:
+            # Plan/trial driven by platform invite code (existing pilot flow)
             sub_plan = invite_code_record.assigned_plan
+            sub_status = "active"
+            period_start = None
+            period_end = None
             if invite_code_record.trial_duration_days:
                 sub_status = "trialing"
                 period_start = datetime.now(timezone.utc)
                 period_end = period_start + timedelta(days=invite_code_record.trial_duration_days)
-
-        new_subscription = Subscription(
-            account_id=new_account.id,
-            plan=sub_plan,
-            status=sub_status,
-            current_period_start=period_start,
-            current_period_end=period_end,
-        )
-        db.add(new_subscription)
+            db.add(Subscription(
+                account_id=new_account.id,
+                plan=sub_plan,
+                status=sub_status,
+                current_period_start=period_start,
+                current_period_end=period_end,
+            ))
+        else:
+            # New self-serve shop — start the standard Pro trial.
+            # start_trial commits internally; flush our pending User/Account changes
+            # first so the FK is satisfied.
+            await db.flush()
+            from app.services.billing import BillingService
+            await BillingService.start_trial(db, new_account.id)
 
     # Mark platform invite code as used
     if invite_code_record: