My impression is completely different, it's less the state but more the media.
Some first standardisations started with the beginning of the printed media, especially Luther's bible translation, then later printed grammar manuals. In the 19th century newspapers and publishing had an impact which streamlined the written word, becoming "Standard German" which through these influences is rather descended from central Germany, not Prussia.
AFAIK the "high" in high German doesn’t come from class but from geographical position - high is more upriver than the low countries in the north.
As for oral dialects: There was no concerted campaign against dialects like in France as far as I know; here it is actual more of a class thing. Again the media plays a role: the rise of radio and television in the latter half of the 20th century has a harmonising effect, deemphasising dialects.
Some first standardisations started with the beginning of the printed media, especially Luther's bible translation, then later printed grammar manuals. In the 19th century newspapers and publishing had an impact which streamlined the written word, becoming "Standard German" which through these influences is rather descended from central Germany, not Prussia.
AFAIK the "high" in high German doesn’t come from class but from geographical position - high is more upriver than the low countries in the north.
As for oral dialects: There was no concerted campaign against dialects like in France as far as I know; here it is actual more of a class thing. Again the media plays a role: the rise of radio and television in the latter half of the 20th century has a harmonising effect, deemphasising dialects.