The idea, that ethnicity is something fixed, something biological, is a bit insulting to the individual, who walks their own way and makes their own decisions. Of course, that doesn't mean, one cannot honour their foreparents and the way they walked.
Again, I've encountered this exact type of description of heritage all over the world. I remember the princess in Saudi Arabia who told me she was a quarter Kuwaiti and an eighth Turkish or something like that. And in the Philippines another girl there told me she was such-and-such a percent Hawaiian, Italian, Spanish, Japanese, and indigenous Filipino. Why is this odd? Let alone ridiculous?
Ethnicity is to identify with a group. A group which then can be attributed shared traits. That can be used to treat or approach a person in a way, that is harmful. It of course does not mean that the notion of Ethnicity itself is insulting.
note the "and/or"... that's important.
A couple years later they both managed to get to the United States on tourist visas. They immediately claimed asylum, it was granted, and within a few years they were American citizens.
Heritage in that your identy is based on where your current way of life comes from.
Culture in that your identity is based on how your engage with your environment in the moment.
So a) is you saying that you, to an extend, identify yourself with your cherokee heritage, even though you do not actively engage with it. B) is DG wondering, why someone would call themself German, when they do not learn German or come to Germany.
If I might offer myself up for contrast: You said you are 25% Cherokee, which does not play a major role in your life. In my case, I only have this 25%, as only one of four grandparents was ever known to me or my parents. It is not sensible to me to talk about my heritage, when I know that this heritage is not based on ancestry but on my own choice. And in that case, what meaning has that 25% ancestry anyway?
Also, of course it has to be said, we are talking about Germany. I know the exact people in my lineage that fought for a government that literally murdered people like me. I do not wish these people to be part of my identy whatsoever.