Replaces the /plan placeholder with a full self-service surface bound to
/api/v1/billing/* on arcadia-core:
- current plan + status + renewal date + manage-billing/cancel actions
- plan picker -> POST /billing/checkout -> redirect to the hosted (mock)
checkout URL -> return reflects the new plan
- invoices table; AUD/GST-aware price formatting
New app/lib/arcadia/billing.ts domain module (mirrors api-keys.ts). The payment
provider is resolved server-side, so this works with the mock today and a real
PSP later with no UI change. Pairs with arcadia-core GET /billing/plans (PR #18).
