Where is the content that is outputted by get_the_archive_description()?

That function starts like this:

function get_the_archive_description() {
    if ( is_author() ) {
        $description = get_the_author_meta( 'description' );
    } elseif ( is_post_type_archive() ) {
        $description = get_the_post_type_description();
    } else {
        $description = term_description();
    }

so you’re looking at get_the_post_type_description().

If you check the docs for register_post_type() you’ll see that description is one of the args that this takes. So you need to either use a plugin/write code to create a place to add this text in the backend, and then dynamically fill that arg with your custom field content, or you need to add the text in code where you’re registering the CPT.