Profile: Francisco Ramón Molina Busquiel

Problem: Using PHP, I would like to know if the current page is a custom post type archive, and I would like to be able to determine the name of the Content Template applied to the current page.

Solution:
Use the native WordPress function is_post_type_archive() to determine if the current page is a post type archive:

if ( is_post_type_archive( 'my-custom-post-type-slug' ) ) {
  // do something
}

Use the wpv_filter_content_template_output filter to determine the assigned Content Template, and assign that value to a global variable. Then access the title of the Content Template post using get_the_title() since Content Templates are technically posts:

add_filter( 'wpv_filter_content_template_output', 'get_content_template_id', 99, 4 );
function get_content_template_id( $content, $template_selected, $id, $kind ) {
    global $current_archive_template_id;   
    $current_archive_template_id = $template_selected; // $template_selected = current Content Template ID
    return $content;
}
// later...
$content_template_title = get_the_title($current_archive_template_id);

Relevant Documentation: https://codex.wordpress.org/Function_Reference/is_post_type_archive
https://toolset.com/documentation/programmer-reference/views-filters/#wpv_filter_content_template_output