With featureFlagSearchExtension on a sharded cluster, $searchBeta (a server-only alias the extension doesn't register) is desugared by mongos into the legacy internal

shape and sent to shards, where the extension's $search mis-parses that wrapper as a user query and forwards it to mongot, which rejects it with Location65330 — while plain $search is unaffected because it's extension-owned on both mongos and shards.