What’s the best way to split admin-only functionality in the theme’s functions.php file?

Question

The way you do it is fine.

Also have a look at how Tom McFarlins WordPress Plugin Boilerplate does it:

if ( is_admin() && ( ! defined( 'DOING_AJAX' ) || ! DOING_AJAX ) ) {    
     require_once( plugin_dir_path( __FILE__ ) . 'admin/class-plugin-name-admin.php' );
     add_action( 'plugins_loaded', array( 'Plugin_Name_Admin', 'get_instance' ) );    
}

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