feat(billing): add useBillingStore and /billing/state integration

T32: Single frontend source of truth for subscription / plan / feature
state. New Zustand `useBillingStore` fetches `/billing/state` (auto-fetch
on login via authStore, reset on logout), exposes `refetch` for
post-Checkout refresh, and is supported by a `useBillingPoll` hook
that re-fetches every 60s while authenticated. The new `billingApi`
client transforms the snake_case backend payload to camelCase at a
single boundary so the rest of the frontend never sees `plan_billing`
or `enabled_features`.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

frontend/src/api/billing.ts

@@ -0,0 +1,27 @@
+import apiClient from './client'
+import type { BillingStateApiResponse, BillingStatePayload } from '@/types'
+
+/**
+ * Single boundary where the snake_case backend payload is transformed
+ * into the camelCase shape used by the rest of the frontend.
+ *
+ * Keeping the transform here means the store, hooks, and components
+ * never see snake_case keys.
+ */
+function transformBillingState(raw: BillingStateApiResponse): BillingStatePayload {
+  return {
+    subscription: raw.subscription ?? null,
+    planBilling: raw.plan_billing ?? null,
+    planLimits: raw.plan_limits ?? {},
+    enabledFeatures: raw.enabled_features ?? {},
+  }
+}
+
+export const billingApi = {
+  async getState(): Promise<BillingStatePayload> {
+    const response = await apiClient.get<BillingStateApiResponse>('/billing/state')
+    return transformBillingState(response.data)
+  },
+}
+
+export default billingApi