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/tests/test_admin_plan_limits.py

@@ -122,9 +122,9 @@ class TestAdminPlanLimits:
     ):
         """PUT /admin/plan-limits upserts a plan_billing row when billing
         fields are included in the body."""
-        # Ensure no plan_billing row exists for "team" yet.
+        # Ensure no plan_billing row exists for "enterprise" yet.
         existing = (await test_db.execute(
-            select(PlanBilling).where(PlanBilling.plan == "team")
+            select(PlanBilling).where(PlanBilling.plan == "enterprise")
         )).scalar_one_or_none()
         if existing is not None:
             await test_db.delete(existing)
@@ -133,7 +133,7 @@ class TestAdminPlanLimits:
         response = await client.put(
             "/api/v1/admin/plan-limits",
             json={
-                "plan": "team",
+                "plan": "enterprise",
                 "max_trees": None,
                 "max_sessions_per_month": None,
                 "max_users": None,
@@ -163,7 +163,7 @@ class TestAdminPlanLimits:
         # Confirm the row was actually persisted.
         await test_db.commit()  # ensure session sees other-session writes
         pb = (await test_db.execute(
-            select(PlanBilling).where(PlanBilling.plan == "team")
+            select(PlanBilling).where(PlanBilling.plan == "enterprise")
         )).scalar_one_or_none()
         assert pb is not None
         assert pb.display_name == "Team"
@@ -179,17 +179,17 @@ class TestAdminPlanLimits:
         plan_billing row when the caller passes explicit nulls. The set of
         guarded fields is {display_name, is_public, is_archived, sort_order}.
         """
-        # Seed a plan_billing row for "team" with non-default values for every
+        # Seed a plan_billing row for "enterprise" with non-default values for every
         # NOT NULL field so we can detect any clobbering.
         existing = (await test_db.execute(
-            select(PlanBilling).where(PlanBilling.plan == "team")
+            select(PlanBilling).where(PlanBilling.plan == "enterprise")
         )).scalar_one_or_none()
         if existing is not None:
             await test_db.delete(existing)
             await test_db.commit()
 
         seeded = PlanBilling(
-            plan="team",
+            plan="enterprise",
             display_name="Team Seeded",
             is_public=False,
             is_archived=True,
@@ -201,7 +201,7 @@ class TestAdminPlanLimits:
         response = await client.put(
             "/api/v1/admin/plan-limits",
             json={
-                "plan": "team",
+                "plan": "enterprise",
                 "max_trees": None,
                 "max_sessions_per_month": None,
                 "max_users": None,
@@ -221,7 +221,7 @@ class TestAdminPlanLimits:
         # Confirm the seeded NOT NULL values were preserved.
         await test_db.commit()  # ensure session sees writes from the request
         pb = (await test_db.execute(
-            select(PlanBilling).where(PlanBilling.plan == "team")
+            select(PlanBilling).where(PlanBilling.plan == "enterprise")
         )).scalar_one_or_none()
         assert pb is not None
         assert pb.display_name == "Team Seeded"