I'm having a hard time finding out about ethno or folk music in the german region (exluding bavaria) and especially about the inner workings of examples of such. I'm especially interested in anything in the prussian region, ethnomusicologist works, music theoretical works, on peasant music, even just genre names, anything really.
This is probably a sore issue. "Volksmusik" is one of the most profitable parts of music/TV business and popular with a large part of the elder generation. But the overwhelming part of it is an artificial creation drawing on traditions of the alpine regions (so outside of Bavaria, you are not really talking as much about "German" but "German-spoken") and other countries like Slovenia (such as the hugely popular "Oberkrainer" music style probably having a lot larger fandom in Germany than in Slovenia itself). If your criterion "not Bavaria" does not mean the political district but the geographic region as such, you'll find some independent forms of folk music in Franconia, and also in "Baden" (the "Baden" in Baden-Württemberg).
The North Sea region sports a variant called "Schiffermusik" which has its origins in seamen music typically played on concertinas. However, the current music style (obviously sporting colorful costumes like all of the big "Volksmusik" business, in this case mimicking idealized variants of sailor gear) tends to use piano accordions for accompaniment.
Outside of the accordion-centric "Volksmusik" directions, brass music is pretty prevalent. The traditional "Schützenvereine" (shooting clubs) tend to focus on garb and traditions from the Kaiserzeit and entertain their own marching bands. The "traditionality" of those is at least so-so, but of course much of the music material has Austrian/Hungarian origin. Prussia has had its own share of military music of course but the GDR would probably have centralized the organization of marching bands.
So there seems to be a large dearth of actual folk music, and part of the reason is that folk music has been absorbed into more intellectual forms of music during Baroque times already: this trend of refining folk tunes that was underlying much of the Renaissance music culture in Western Europe really took off in Germany. Dances and tunes were integrated into Baroque music, and in the Romantic era, a lot of folk songs were sucked into more complex art forms as well, like Brahms with his Volkslieder.
You'll still find traditional organizations like "Männergesangsvereine" (men's singing clubs) with specializations like "Grubenchöre" (miner's choirs) but their popularity and renown, even though they stay around with at least some stubbornness, tends to be quite lower than that of the artificial "Volksmusik" creation. They tend to focus on simple multi-voice arrangements of traditional tunes and religious songs: "Silcher" is quite more a household name there than "Brahms" or "Bach" since the latter are feared for their complexity.
So for actual folk music rather than a synthesized "Volksmusik" created and maintained for feeding a particular entertainment market sector, you'll have to look closer. Media coverage and renown is not overwhelming.
Please note that the Germanic folk/ethnic culture present in the Prussia would not (IMO) significantly differ from other main regions of Germany since the German speaking population was composed of colonists (most of them migrated quite late). The original folk culture present in this region was mostly related to original Baltic ethnicity or other groups like Mazur culture. The official Prussian "state" culture was military driven and mono-ideological and I would not expect that you find any major ethnic influence in Prussian (German) music from this period. The Baltic people were in fact erased from the region by Prussian state, given that I am skeptical any music material may be find.