Are the nutritionist training courses with a certificate or diploma also federally recognized?

No.

You can only obtain federally recognized qualifications as a nutritionist with a Bachelor of Science (BSc) in Nutrition and Dietetics (UAS) and a subsequent Master's degree, such as the Master of Science (MSc) in Life Sciences - Food, Nutrition and Health (UAS).

Certificate courses or diploma courses award internal school qualifications that are not subject to any official regulation and are therefore not federally recognized. Nevertheless, they can provide competent training.