I have a custom post type called podcast_episode registered in functions.php.

I also have a template ready called single-podcast_episode.php

When I create a new podcast_episode post, the classic post editor has the Default template selected. If I click the dropdown, I can see my single-podcast_episode template.

How can I set it up so that the single-podcast_episode template is the default for podcast_episode posts?

I.e. How can I change the default template for a custom post type?

I would have thought according to the custom post type template files doc, the template hierarchy of my single-podcast_episode.php would be enough, although maybe that only applies to the frontend?

Create custom post type code if needed:

function _s_create_custom_post_types() {
    register_post_type(
        'podcast_episode',
        array(
            'labels' => array(
                'name' => __('Podcast Episodes'),
                'singular_name' => __('Podcast Episode'),
                'add_new' => __('Add New'),
                'add_new_item' => __('Add New Podcast Episode'),
                'view_item' => __('View Item'),
                'edit_item' => __('Edit Item'),
                'search_items' => __('Search Items'),
                'not_found' => __('Not Found'),
                'not_found_in_trash' => __('Not Found in Trash')
            ),
            'public' => true,
            'hierarchical' => true,
            'supports' => array('title', 'editor'),
            'rewrite' => array(
                'slug' => 'podcast/%taxonomy_name%',
            ),
            'taxonomies' => array('podcast_episode'),
            'query_var' => true,
            'supports' => array('title', 'editor', 'thumbnail'),
        )
    );
}
add_action('init', '_s_create_custom_post_types');