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

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

backend/app/services/billing.py

@@ -0,0 +1,36 @@
+"""Single billing service module. Stripe is the only impl — no provider
+abstraction. Account row is canonical local state; Stripe is canonical
+remote state; the webhook handler bridges the two."""
+from datetime import datetime, timezone, timedelta
+from sqlalchemy import select
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from app.models.subscription import Subscription
+
+
+TRIAL_DAYS = 14
+
+
+class BillingService:
+    @staticmethod
+    async def start_trial(db: AsyncSession, account_id) -> Subscription:
+        """Idempotent. Creates a trialing Subscription on Pro for the account if
+        one doesn't exist; otherwise returns the existing row."""
+        result = await db.execute(
+            select(Subscription).where(Subscription.account_id == account_id)
+        )
+        existing = result.scalar_one_or_none()
+        if existing is not None:
+            return existing
+
+        sub = Subscription(
+            account_id=account_id,
+            plan="pro",
+            status="trialing",
+            current_period_start=datetime.now(timezone.utc),
+            current_period_end=datetime.now(timezone.utc) + timedelta(days=TRIAL_DAYS),
+        )
+        db.add(sub)
+        await db.commit()
+        await db.refresh(sub)
+        return sub