Fixes regression introduced in [36414] where the nonce for listing available nav menu items was updated to use the new centralized location at `wp.customize.settings.nonce`, but the nonce for search did not get updated.
See #35617.
Built from https://develop.svn.wordpress.org/trunk@36432
git-svn-id: http://core.svn.wordpress.org/trunk@36399 1a063a9b-81f0-0310-95a4-ce76da25c4cd