How do I change the Go To Categories link in the term_updated_messages

If you mean, how to change the link’s text, then you can change it when you register your taxonomy, by setting the back_to_items label to whatever text you like. Excerpt from the documentation:

  • back_to_items’ – the text displayed after a term has been updated for a link back to main index. Default is __( '← Back to tags' ) or __( '← Back to categories' )

So for example:

register_taxonomy( 'shows', 'post', array(
    'public'            => true,
    'labels'            => array(
        'name'          => 'Shows',
        'singular_name' => 'Show',
        'back_to_items' => __( '← Go to Shows', 'text-domain' ),
        // other labels
    'show_admin_column' => true,
    // your other args
) );

If you are unable to change/set the label during the taxonomy registration, e.g. because the taxonomy is being registered by a plugin, you can use the registered_taxonomy_<taxonomy> or registered_taxonomy hook to override the taxonomy labels (and other args).