Based on that definition Dutch also wouldn’t be a different language but a dialect within High German called Franconian.
Now try telling Dutch people that they don’t actually have their own language and are all speaking Low Country German and see what happens…
Most distinctions between dialects and languages are socio-political and not linguistic.
There is a similar continuum between North/Low German and Frisian. Yet you cross a border and just like Dutch/Franconian it’s no longer a dialect but a different language.
According to Wikipedia, Franconian is split between Low Franconian dialects, including Dutch, and the others, which underwent the same consonant shift as the High German languages. But I agree that the boundaries of languages are not purely linguistic.
I don't think you have that quite right. Alemannic does not include Standard High German. Alemannic is a group of High German dialects in the southwestern German-speaking areas.
>>The High German languages (German: hochdeutsche Mundarten, i.e. High German dialects), or simply High German (Hochdeutsch) – not to be confused with Standard High German which is commonly also called "High German"
Not a different language but a dialect-group within high german called Alemanic:
https://en.wikipedia.org/wiki/Alemannic_German
Also interesting:
https://en.wikipedia.org/wiki/High_German_languages