How to make WordPress Plugin run on single specific Admin Page

You should use the load-edit.php action hook, and check for your post type (untested):

add_action( 'load-edit.php', static function () {
    $screen = get_current_screen();

    if ( empty( $screen->post_type ) || 'myposttype' !== $screen->post_type ) {
        return;
    }

    new the_function();
} );

You could also use the current_screen hook, but load-edit.php seems more correct.