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/alembic/versions/4ce3e594cb87_add_starter_rename_team_to_enterprise.py

@@ -0,0 +1,84 @@
+"""add_starter_rename_team_to_enterprise
+
+Revision ID: 4ce3e594cb87
+Revises: c6cbfc534fad
+Create Date: 2026-05-07 19:36:27.172082
+
+Plan tier taxonomy reconciliation. Marketing surface and Stripe products
+named "Starter / Pro / Enterprise"; backend was on "free / pro / team".
+This migration:
+
+  1. Defensively migrates any existing subscriptions on plan='team' to
+     plan='enterprise' (dev has zero such rows; prod is expected to have
+     none, but the UPDATE is safe and idempotent).
+  2. Renames the plan_limits row 'team' -> 'enterprise'. plan_billing
+     and plan_feature_defaults are FK-referenced but currently empty;
+     the rename works because PostgreSQL allows updating PK values when
+     no FK rows reference them.
+  3. Inserts a new plan_limits row for 'starter' between free and pro.
+
+Resource visibility (Tree.visibility, StepLibrary.visibility) also uses
+the string 'team' for "shared with my account" — that is a separate
+domain and is intentionally not touched.
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+
+revision: str = '4ce3e594cb87'
+down_revision: Union[str, None] = 'c6cbfc534fad'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.execute("UPDATE subscriptions SET plan = 'enterprise' WHERE plan = 'team'")
+    op.execute("UPDATE plan_limits SET plan = 'enterprise' WHERE plan = 'team'")
+    op.execute("""
+        INSERT INTO plan_limits (
+            plan,
+            max_trees,
+            max_sessions_per_month,
+            max_users,
+            custom_branding,
+            priority_support,
+            export_formats,
+            max_ai_builds_per_month,
+            max_ai_builds_per_24h,
+            kb_accelerator_enabled,
+            kb_max_lifetime_conversions,
+            kb_batch_max_size,
+            kb_allowed_formats,
+            kb_detailed_analysis,
+            kb_conversational_refinement,
+            kb_step_library_matching,
+            kb_history_limit
+        ) VALUES (
+            'starter',
+            10,
+            75,
+            1,
+            FALSE,
+            FALSE,
+            '["markdown", "text", "html"]'::jsonb,
+            15,
+            5,
+            FALSE,
+            NULL,
+            NULL,
+            '["txt", "paste", "md"]'::jsonb,
+            FALSE,
+            FALSE,
+            FALSE,
+            NULL
+        )
+        ON CONFLICT (plan) DO NOTHING
+    """)
+
+
+def downgrade() -> None:
+    op.execute("DELETE FROM plan_limits WHERE plan = 'starter'")
+    op.execute("UPDATE plan_limits SET plan = 'team' WHERE plan = 'enterprise'")
+    op.execute("UPDATE subscriptions SET plan = 'team' WHERE plan = 'enterprise'")