My Dad's family emigrated from Schleswig-Holstein area on the Jutland Peninsula. The first arrived in 1868. I'm told that they spoke a dialect of German that was not common. In fact when my Dad joined the Army Air Corps, an officer said he'd heard it only one time before.
Since the Jutland changed hands, politically, so many times between Denmark and Germany I've always wondered if we are Danish or German. I was always told German because gr g-pa travelled from Hamburg. Is one's nationality defined in political boundary terms or is it a cultural definition.
It would depend heavily on what your father's family thought they were. The family name would be your biggest clue -- if it's a German name, they were likely ethnically/culturally German. Since you were told he came from Hamburg, that's your answer.
That whole area traded hands a lot, leading to considerable intermixture and people will still identify as their base ethnic group. For example, there are lots of ethnic Swedes (many of whom still speak Swedish) living in Finland who are citizens. While they are Finnish citizens, they are very likely to have relatives in Sweden and act culturally like Swedes. Same with ethnic Russians in the Balts (although that's a much more fraught relationship.
To answer your question, nationality tends to be based on political borders, while ethnicity is based on cultural and blood ties.
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If you ask the Germans, they would say you were German. After the wall came down, Germany welcomed with full citizenship anyone of German heritage who had been separated by the iron curtain. So there were people from Poland and Czechoslovakia, etc., who were ethnic Germans who were repatriated. So I would say German, since it was a German dialect they spoke.
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The family always said we were German. Just to clarify...gr g-pa travelled from S-H to Hamburg to catch the boat. He wasn't technically from Hamburg.
We weren't brought up with a particular culture or ethnicity...in the way of foods or customs. Dad's people settled on the Iowa frontier and were farmers or tailors. Basic peasants...affectionately termed. They ate what they had and made do for the rest. Dad did tell of having candles on their Christmas tree for just one hour or so on Christmas Eve. Not sure if that's a particularly German custom or just a basic European custom.
Anyway, was just wondering. They are all long dead. No one to ask anymore. :-(