Meta Box

1) I intentionally set both options for std and problem was in empty value. So, now works PERFECT. Thanks.

2) I'm afraid how I will need to do it with Custom Taxonomy, as it looks how JetSmartFilters supports only CFds created by its own JetEngine (where I cannot set auto-populate). So, please, if you can, help here also. Code is (just author, as I guess that I will figure than):

function your_prefix_register_taxonomy() {

    $args = array (
        'label' => esc_html__( 'Autores de la publicación', 'text-domain' ),
        'labels' => array(
            'menu_name' => esc_html__( 'Autores de la publicación', 'text-domain' ),
            'all_items' => esc_html__( 'All Autores de la publicación', 'text-domain' ),
            'edit_item' => esc_html__( 'Edit Autor de la publicación', 'text-domain' ),
            'view_item' => esc_html__( 'View Autor de la publicación', 'text-domain' ),
            'update_item' => esc_html__( 'Update Autor de la publicación', 'text-domain' ),
            'add_new_item' => esc_html__( 'Add new Autor de la publicación', 'text-domain' ),
            'new_item_name' => esc_html__( 'New Autor de la publicación', 'text-domain' ),
            'parent_item' => esc_html__( 'Parent Autor de la publicación', 'text-domain' ),
            'parent_item_colon' => esc_html__( 'Parent Autor de la publicación:', 'text-domain' ),
            'search_items' => esc_html__( 'Search Autores de la publicación', 'text-domain' ),
            'popular_items' => esc_html__( 'Popular Autores de la publicación', 'text-domain' ),
            'separate_items_with_commas' => esc_html__( 'Separate Autores de la publicación with commas', 'text-domain' ),
            'add_or_remove_items' => esc_html__( 'Add or remove Autores de la publicación', 'text-domain' ),
            'choose_from_most_used' => esc_html__( 'Choose most used Autores de la publicación', 'text-domain' ),
            'not_found' => esc_html__( 'No Autores de la publicación found', 'text-domain' ),
            'name' => esc_html__( 'Autores de la publicación', 'text-domain' ),
            'singular_name' => esc_html__( 'Autor de la publicación', 'text-domain' ),
        ),
        'public' => true,
        'show_ui' => true,
        'show_in_menu' => true,
        'show_in_nav_menus' => true,
        'show_tagcloud' => false,
        'show_in_quick_edit' => false,
        'show_admin_column' => false,
        'show_in_rest' => true,
        'hierarchical' => false,
        'query_var' => true,
        'sort' => false,
        'rewrite_no_front' => false,
        'rewrite_hierarchical' => false,
        'rewrite' => true,
    );

    register_taxonomy( 'autor-de-la-publicacion', array( 'noticias', 'articulos', 'cuentos', 'estudios', 'regalos', 'encuestas', 'ejercicios-web', 'podcasts', 'webcasts', 'seminarios-web', 'reciclados' ), $args );
}
add_action( 'init', 'your_prefix_register_taxonomy', 0 );

1) REQUIRED

Yes, I'm using Gutenberg. However, I figured (I guess correctly) how it is 100% irrelevant in my case as it should to be auto-populated.

2) STD

You are right that I missed, but it still not works. I tried with both version (what I know) to insert it, but not working. Code is (intentionally mixed two variations) as

https://pastebin.com/kUNCMQpJ

3) TAXONOMY

You missed that I would actually like much more if that will be taxonomy solution, than custom fields. Is it possible to do with taxonomy (how should to look code for author (ie)?

4) FILTRATION

You are right. That is certainly best option vs pricing (my opinion), but as blog is on Elementor and CrocoBlocks grounded (in any case), natural solution is to using JetSmartFilters as part of bundle.

I forgot, if it is easier for taxonomy, works also with CrocoBlocks.

It is not a theme issue (looks for me), as I tried on default (19), Genesis, OceanWP, GeneratePress and Astra.

So, to repeat, I consider it MetaBox issue as:

1) I checked on right metabox that I want to associate categories and tags to my CPT.
2) Code (PHP) is wrote that action in order.
3) Custom Categories created by MB can be listed (displayed).
4) Custom 'tags' (non hierarchical taxonomy) created by MB can be listed (displayed).

SOLUTION

So, I simply deactivated Categories and Tags, plus created replacements by MB and it works. However, it is not a topic, as I ask why it not working?

By the way, your new versions have a bug on repeated License requests and boxes.