feat(billing): reconcile plan taxonomy and add Stripe sync script

The marketing surface (PricingPage, Stripe products) was wired for
"Starter / Pro / Enterprise" while the backend was on "free / pro / team",
leaving plan_billing unseeded and BillingPlan accepting a literal that
violated the FK to plan_limits.

This change:

- Migration 4ce3e594cb87: defensive UPDATE of any subscriptions on
  plan='team' to 'enterprise' (dev has zero), renames the plan_limits
  row team -> enterprise, inserts a starter row with caps interpolated
  between free and pro (max_trees=10, sessions=75, ai=15/mo).
- Renames the plan tier across schemas (invite_code, billing, admin,
  subscription comment), is_paid/has_pro_entitlement checks in the
  Subscription model, admin/admin_dashboard plan validators, and the
  frontend useSubscription isPaidPlan check. Resource visibility uses
  the same string 'team' in a separate domain (Tree/StepLibrary
  visibility) and is intentionally untouched.
- New backend/scripts/sync_stripe_plan_ids.py: idempotent upsert of
  plan_billing rows from Stripe products by exact name match. Picks
  the active monthly recurring price for tiers that have one; leaves
  annual fields NULL by design. Works against test or live keys.
- Test fixture updates: conftest seeds the new taxonomy, the public
  plans helper is a true upsert so tests can override max_users, and
  team -> enterprise across test_admin_plan_limits and test_invite_plan.

Verified: 86/86 passing across the subscription/billing/plan/invite/
admin sweep; sync script run against test mode populates plan_billing
correctly for all three tiers.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/app/api/endpoints/admin.py

@@ -972,7 +972,7 @@ async def update_user_plan(
     current_user: Annotated[User, Depends(require_admin)],
 ):
     """Change a user's subscription plan (super admin only)."""
-    if data.plan not in ("free", "pro", "team"):
+    if data.plan not in ("free", "pro", "starter", "enterprise"):
         raise HTTPException(status_code=status.HTTP_400_BAD_REQUEST, detail="Invalid plan")
     user, subscription = await _get_user_subscription(user_id, db)
     old_plan = subscription.plan
@@ -991,7 +991,7 @@ async def update_account_plan(
     current_user: Annotated[User, Depends(require_admin)],
 ):
     """Change an account subscription plan (super admin only)."""
-    if data.plan not in ("free", "pro", "team"):
+    if data.plan not in ("free", "pro", "starter", "enterprise"):
         raise HTTPException(status_code=status.HTTP_400_BAD_REQUEST, detail="Invalid plan")
     account, subscription = await _get_account_subscription(account_id, db)
     old_plan = subscription.plan

backend/app/api/endpoints/admin_dashboard.py

@@ -28,7 +28,7 @@ async def get_dashboard_metrics(
     ) or 0
     paid_accounts = await db.scalar(
         select(func.count()).select_from(Subscription).where(
-            Subscription.plan.in_(["pro", "team"])
+            Subscription.plan.in_(["pro", "starter", "enterprise"])
         )
     ) or 0
     total_trees = await db.scalar(