Trying to add a page template for my custom post type from a plugin, but it will not display in the template dropdown unless file is in theme

The filter hook you’re using is theme_<post type>_templates, which means that the <post type> part is dynamic and it’s the post type in which you want the custom template be added to the Template dropdown. So since the template is enabled for three post types, you would do so to add the template to the dropdown:

add_filter( 'theme_publication_templates', 'wp234234_theme_page_templates' ); // publication CPT
add_filter( 'theme_page_templates', 'wp234234_theme_page_templates' );        // regular Pages
add_filter( 'theme_post_templates', 'wp234234_theme_page_templates' );        // regular Posts

Or you can instead use the theme_templates hook: ^{( Note: This hook runs before the ones above. )}

add_filter( 'theme_templates', 'wpse_387479_theme_templates', 10, 4 );
function wpse_387479_theme_templates( $post_templates, $theme, $post, $post_type ) {
    if ( in_array( $post_type, array( 'publication', 'page', 'post' ) ) ) {
        $post_templates['/absolute/path/to/template-publication-special.php'] = 'Publication special';
    }

    return $post_templates;
}

PS: Just change the “publication” to the correct post type, if what I used is wrong?