How to create taxonomy values for pages and list them in wp-admin

This is definitely possible, and pretty easy too!

If you’d like to register an existing taxonomy (i.e. category) with an existing post type (i.e page), register_taxonomy_for_object_type() can be used. E.g.:

add_action( 'init', 'wpse_register_category_tax_for_page' );
function wpse_register_category_tax_for_page() {
    $taxonomy    = 'category';
    $object_type="page";

    register_taxonomy_for_object_type( $taxonomy, $object_type );
}

A new taxonomy can be created and associated with an new/existing post type as well. In this example, the taxonomy classification is associated with the existing post type, page:

add_action( 'init', 'wpse_register_custom_taxonomy', 0 );
function wpse_register_custom_taxonomy() {
    // Arguments for register_taxonomy().
    $args = [
        'public'            => true,
        'hierarchical'      => true,
        'label'             => __( 'Classification', 'textdomain' ),
        'show_ui'           => true,
        'show_admin_column' => true,
        'query_var'         => 'classification',
        'rewrite'           => [ 'slug' => 'classification' ],
    ];

    // Array of post types to associate with this taxonomy.
    $post_types = [ 'page' ];

    register_taxonomy( 'classification', $post_types, $args );
}

Note that the parameter $show_admin_column has been set to true here. This will ensure that the taxonomy column will be added to the /wp-admin/edit.php?post_type=page screen.

Let’s pretend that some other plugin registered the classification taxonomy and set the $show_admin_column parameter to false. We can use the register_taxonomy_args to override the original setting and ensure that the taxonomy appears in the admin columns:

add_filter( 'register_taxonomy_args', 'wpse_edit_taxonomy_args', 10, 3 );
function wpse_edit_taxonomy_args( $args, $taxonomy, $object_type ) {
    // Array of taxonomies to change arguments on.
    $taxonomies = [
        'classification',
    ];

    // Set $show_admin_column to true.
    if ( in_array( $taxonomy, $taxonomies ) ) {
        $args[ 'show_admin_column' ] = true;
    }

    return $args;
}