Register Page Template from Plugin

You misunderstand what page_template does. It does not create a new template that you will “show up” somewhere and that you can use. It replaces the page.php template provided by the theme.

I think that what you want is template_redirect:

function custom_page_template( $page_template ) {
  if (is_home()) {
    get_header();
    echo 'do stuff';
    get_footer();
  }
}
add_filter( 'template_redirect', 'custom_page_template' );

Or template_include:

function custom_page_template( $page_template ) {
  if (is_home()) {
    $page_template = plugin_dir_path( __FILE__ ) . 'custom-page-template.php';
    return $page_template;
  }
}
add_filter( 'template_include', 'custom_page_template' );