Expose gateway billing flows from the synced server baseline

The preserved local work adds PopiNewAPI billing checkout, gateway account binding, and matching web console/pricing surfaces on top of the current test-server baseline. During the merge, the start-end video helpers from the deployed baseline were kept alongside the actionGenerate prompt handling from the WIP.

Constraint: Current usable baseline is 7054436, already deployed on the test server.

Rejected: Commit the WIP before syncing the baseline | would have hidden conflicts with the deployed start-end-frame changes.

Confidence: medium

Scope-risk: broad

Directive: Do not deploy this commit to the test server without rechecking gateway credentials and billing checkout behavior in that environment.

Tested: go test ./...

Tested: make build

Tested: cd web && npm run build

web/components/billing-page-state.tsx

@@ -0,0 +1,35 @@
+"use client";
+
+import { useEffect } from "react";
+import { usePathname, useRouter, useSearchParams } from "next/navigation";
+
+const BILLING_STATE_KEY = "popiart-billing-page-state";
+
+export function BillingPageState() {
+  const pathname = usePathname();
+  const router = useRouter();
+  const searchParams = useSearchParams();
+
+  useEffect(() => {
+    const hasQuery = searchParams.toString().length > 0;
+    if (hasQuery) {
+      try {
+        window.sessionStorage.setItem(BILLING_STATE_KEY, searchParams.toString());
+      } catch {
+        // Ignore storage write failures.
+      }
+      return;
+    }
+
+    try {
+      const stored = window.sessionStorage.getItem(BILLING_STATE_KEY);
+      if (stored) {
+        router.replace(`${pathname}?${stored}`);
+      }
+    } catch {
+      // Ignore storage read failures.
+    }
+  }, [pathname, router, searchParams]);
+
+  return null;
+}