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_invite_plan.py

@@ -49,7 +49,7 @@ class TestInviteCodeCreation:
     ):
         response = await client.post(
             "/api/v1/invites",
-            json={"assigned_plan": "team", "email": "beta@example.com"},
+            json={"assigned_plan": "enterprise", "email": "beta@example.com"},
             headers=admin_auth_headers,
         )
         assert response.status_code == 201
@@ -149,7 +149,7 @@ class TestRegistrationWithInvitePlan:
         # Create team invite without trial
         resp = await client.post(
             "/api/v1/invites",
-            json={"assigned_plan": "team"},
+            json={"assigned_plan": "enterprise"},
             headers=admin_auth_headers,
         )
         code = resp.json()["code"]
@@ -172,7 +172,7 @@ class TestRegistrationWithInvitePlan:
         sub = (await test_db.execute(
             select(Subscription).where(Subscription.account_id == user.account_id)
         )).scalar_one()
-        assert sub.plan == "team"
+        assert sub.plan == "enterprise"
         assert sub.status == "active"