This code will help you to change base slug `courses` to your preferred slug, replace `example-course-slug` with your own slug.

tutor-lms-change-default-course-base-slug

add_filter('tutor_courses_base_slug', 'change_tutor_course_slug');
/**
 * @param $slug
 * @return string
 */
if ( ! function_exists('change_tutor_course_slug')){
    function change_tutor_course_slug($slug){
        $slug = 'example-course-slug';
        return $slug;
    }
}

Does not work on my end. The lessons can be changed in the setup, but the 'courses' slug stays the same after using the filter with 'kurse'. Any ideas why?

Try this

add_filter( 'register_post_type_args', 'tutor_register_post_type_args', 10, 2 );
function tutor_register_post_type_args( $args, $post_type ) {
if ( 'courses' === $post_type ) {
$args['rewrite']['slug'] = 'customslug'; //here add your new slug
}
return $args;
}

Thank you that works. However, the lessons still point to the 'courses' slug. I already flushed the permalinks twice. Any ideas?

Try this, it should work better: https://github.com/martinmaiolo/tutor-LMS/blob/main/tutor-lms-change-default-course-base-slug

add_filter('tutor_courses_base_slug', 'change_tutor_course_slug');
/**
 * @param $slug
 * @return string
 */
if ( ! function_exists('change_tutor_course_slug')){
    function change_tutor_course_slug($slug){
        $slug = 'example-course-slug';
        return $slug;
    }
}