I haven’t heard “mixed race†in a long time.
That's odd because there are so many mixed-race people these days and almost all identify as people of color. I don't think Harris identifies as Black, even though others might see her that way.
Obama on the other hand seems to identify as Black even though he is mixed and raised mostly by his white family.
In the greater scheme of things, it makes less and less difference every year as the stigma around inter-racial breeding/fraternizing has mostly gone away. As time goes on there will be less and less need to define folks by race as well as by name.