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/hooks/useBillingPoll.ts

@@ -0,0 +1,32 @@
+import { useEffect } from 'react'
+import { useAuthStore } from '@/store/authStore'
+import { useBillingStore } from '@/store/billingStore'
+
+const POLL_INTERVAL_MS = 60_000
+
+/**
+ * Re-fetches billing state every 60s while a user is logged in.
+ *
+ * Mount once at the top of the authenticated dashboard tree. Polling
+ * automatically pauses when the auth store reports no logged-in user.
+ *
+ * Note: this is a v1 simple-interval implementation; a later task may
+ * swap to SSE / visibility-aware polling.
+ */
+export function useBillingPoll(): void {
+  const isAuthenticated = useAuthStore((s) => s.isAuthenticated)
+
+  useEffect(() => {
+    if (!isAuthenticated) return
+
+    const id = window.setInterval(() => {
+      void useBillingStore.getState().refetch()
+    }, POLL_INTERVAL_MS)
+
+    return () => {
+      window.clearInterval(id)
+    }
+  }, [isAuthenticated])
+}
+
+export default useBillingPoll