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.
Prussia, let alone Prussian “identity” is not something that existed well into the mid to late modern era.