Show tags for each entry
You're very close. Change "set tag" to "set tags" so you have:

{% set tags = entry.projektart %}


And then loop through the tags:

{% for tag in tags %}
    {{ tag }}
{% else %}
    No tags found
{% endfor %}


You could also simplify this and instead of setting the "tags" variable you could write the following:

{% for tag in entry.projektart %}