Change URL structure of subcategory archive pages

You answered your own question yourself.

You want links to custom categories to look like this

{taxonomy_slug}/{parent_term}/{child_term}/{grandchild_term}/

so you should pay attention to two parameters in the register_taxonomy() arguments: hierarchical and rewrite.

$args = [
    'hierarchical' => true,      // <-- term may have a parent
    'labels'       => $labels,
    'rewrite'      => [
        // hierarchical urls, defaults to FALSE
        'hierarchical' => true,  // <-- 
    ]    
];

Your custom taxonomy is created by the parent theme, so to change it, use the register_taxonomy_args filter:

add_filter( 'register_taxonomy_args', 'se344007_mytax_args', 10, 2 );
function se344007_mytax_args( $args, $taxonomy )
{
    if ( 'mytax' !== $taxonomy ) {
        return $args;
    }    
    // it looks like it's already set up by parent theme
    // $args['hierarchical'] = true;

    if ( !is_array($args['rewrite']) )
        $args['rewrite'] = [];
    $args['rewrite']['hierarchical'] = true;

    return $args;      
}

When you register custom taxonomy, the default link to term (custom category)
is {taxonomy_slug}/{child_term_slug} even if taxonomy is hierarchical, because
by default, the created links are not hierarchical ( $args[‘rewrite’][‘hierarchical’] = false ).