I don't like answering a question with a question but - how do you want to define ethnicity? Go back far enough and we are all, every single one of us, 100% African. Most people tend to refer to baseline their ethnicity a little closer than that! But even if you make an arbitrary choice of a specific, recent generation, the ethnicity might change on the generation before that. In this case, I guess I'm defining "ethnicity" as country of origin.
The DNA approach purports to come up with a quantitative derivation of ethnicity - yet all it actually measures is the similarity of your DNA to the DNA of people from those areas living today.
If you look at the percentage DNA that you inherit from various generations, see https://dna-explained.com/2017/06/27/ancestral-dna-percentages-how-much-of-them-is-in-you/ then at only 7 generations back, the average DNA that you might inherit from someone on that generation is less than 1% and is probably lost in the statistical noise and undetectable.
So DNA estimates of ethnicity are not going to catch minor contributions. But 7 generations back isn't that far back (5G grandparents, as I recollect) and we are all of us liable to make a fuss about a really interesting 6G-GF (say) - I know that I do!
What I guess that I'm saying is that ethnicity is always relative - it depends on which generation you're looking at, and can alter on the next generation back. There isn't a fixed definition and the methods for measuring via DNA are defeated by statistical reality. Best to keep to the paper trail in my view.