Or more likely Prussian, or some other pre-modern political identity. I had the chance to visit a museum outlining the history of the German region and it was a shock to me, even coming from a background as a student of ancient China, how many iterations of how many petty polities existed in this area. Mind boggling. My takeaway: the modern 'nation state' cultural notion is a poor ally in examining the history of the region of modern Germany and its surroundings prior to the 20th century. Shifting alliances of nominally independent city-states combined with evidence toward enthusiastic adoption of distributed printing and popular literacy could be argued to underpin some of the more positive ideals of the EU today, despite the negative interludes.
Yes, it's a relatively late concept, but one could rationally argue it's objectively more correct than 'German' in default modern interpretation, both spatially in that it additionally encompasses what is now western Poland, and temporally in that it is closer to the timeframe in question. As for identity, this can be argued until the cows come home, but many Jews served in the Prussian army (google suggests 100,000-150,000) and you don't put your life on the line without some sense of connection. Little did they know their families would soon be killed by the successor of the very state they had fought to protect.
Prussia was a state that included plenty of culturally in no way Prussian territories in the 1800s.
Calling someone from Cologne Prussian was about as silly as claiming that Belgian Walloons were Dutch prior to 1830. Most people who lived in the Kingdom of Prussia in the early 1900s weren’t really Prussian in most senses.
There was a large population of Jews in Berlin but most of the remaining ones lived in the Rhineland, Westphalia etc.
