perf(i18n): stop serializing the full catalogue on public pages

The root layout fed the entire ~254 KB message catalogue to
NextIntlClientProvider, which serializes it into the RSC payload of every
page. A public page only reads ~59 KB of it; the ~195 KB difference is staff
tool copy that only /admin, /admin-next and /mod ever render.

The root provider now installs the reduced catalogue and each staff route
group re-installs the full one, since a nested NextIntlClientProvider replaces
the parent message set rather than merging into it. pages.admin.actions stays
public because the shared useServerAction hook runs on public pages too.

Measured: 253 KB -> 59 KB of messages per public page (raw JSON).

Guard tests cover all three halves: the root keeps using the reduced
catalogue, every staff layout installs its own full provider, and no public
tree reads a staff-only namespace.

src/app/admin-next/layout.tsx

@@ -1,4 +1,6 @@
 import { notFound } from "next/navigation";
+import { NextIntlClientProvider } from "next-intl";
+import { getLocale, getMessages } from "next-intl/server";
 import type { ReactNode } from "react";
 import { env } from "@/env";
 import { isHousekeepingPreviewEnabled } from "@/features/housekeeping/foundation/preview-gate";
@@ -27,5 +29,13 @@ export default async function AdminNextLayout({
 		notFound();
 	}
 
-	return children;
+	// Staff tree: re-install the full catalogue the root layout scopes down to
+	// the public subset (nested providers replace the parent set).
+	const [locale, messages] = await Promise.all([getLocale(), getMessages()]);
+
+	return (
+		<NextIntlClientProvider locale={locale} messages={messages}>
+			{children}
+		</NextIntlClientProvider>
+	);
 }