feat(admin): extend /admin/plan-limits to manage plan_billing fields

Task 30 of self-serve signup Phase 2. Super-admins can now manage Stripe
IDs, display names, prices, and public/archived flags via the existing
admin plan-limits endpoints.

- GET /admin/plan-limits now outer-joins plan_billing and returns
  merged PlanLimitWithBillingResponse rows. Plans without a
  plan_billing row return None for the billing fields.
- PUT /admin/plan-limits accepts the new optional billing fields and
  upserts plan_billing in the same transaction. If no plan_billing
  row exists for the plan and the body includes any billing field, a
  row is created (display_name defaults to plan.capitalize() when
  omitted; display_name is never NULLed out on an existing row).
- After commit, the handler queries account_ids on the affected plan
  and calls BillingService.invalidate_billing_cache(account_ids).
  This is a no-op stub today (logs only) — there's no in-process
  billing cache yet. TODO comment marks the wire-up point.
- 3 new integration tests cover GET-with-billing-present, PUT creating
  a plan_billing row, and the invalidation hook being awaited with a
  list of account_ids.

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

backend/app/services/billing.py

@@ -1,6 +1,7 @@
 """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."""
+import logging
 from datetime import datetime, timezone, timedelta
 
 import stripe
@@ -17,8 +18,32 @@ from app.models.subscription import Subscription
 
 TRIAL_DAYS = 14
 
+logger = logging.getLogger(__name__)
+
 
 class BillingService:
+    @staticmethod
+    async def invalidate_billing_cache(account_ids) -> None:
+        """No-op stub for future in-process billing cache invalidation.
+
+        Today there is no `app.state.billing_cache` — `BillingService.get_billing_state`
+        always reads fresh from the DB. Call sites that mutate plan/feature data
+        invoke this hook so that wiring is in place when an in-process cache is
+        added later. Until then, this just logs.
+
+        TODO: when an in-process billing cache (e.g. `app.state.billing_cache`)
+        is introduced, evict entries for the given account_ids here.
+        """
+        try:
+            count = len(list(account_ids))
+        except TypeError:
+            count = -1
+        logger.debug(
+            "BillingService.invalidate_billing_cache called for %d account(s) "
+            "(no-op stub — wire to app.state.billing_cache when added)",
+            count,
+        )
+
     @staticmethod
     async def start_trial(db: AsyncSession, account_id) -> Subscription:
         """Idempotent. Creates a trialing Subscription on Pro for the account if