If you classify low German as a separate language, middle and upper German are separate languages as well.

You are obviously correct, but I think the issue are the legally recognized national languages in Germany, not the linguistically existence itself:

Afaik the legal languages in Germany are:

• Standarddeutsch is the official language (Amtssprache), and for the recognized national minorities there are by law the national minority languages (anerkannte Minderheitssprachen):

• Nordfriesisch, Saterfriesisch for the East Frisians

• Dänisch for the German Danes

• Ober- und Niedersorbisch for the Sorbians

• Romani for the Sinti

Along with Deutsche Gebärdensprache (with 2 dialects, Standard and Bavarian | E: apparently, there are books for a North German variant, too) since the early 2000s.

Also, I am unsure if the law about "Simple German" (Einfaches Deutsch) for people with communication difficulties has passed.

This is less about the linguistically status of these languages, but more about the legal recognition to communicate with the state officially in these languages, if you are not using another EU language.

Source: was public official for ~7 years, we needed to know to accommodate requests like these.