Thus using “race” is biologically ambiguous and “ethnic groups” should be preferred, however it is still very well socially defined.

"Ethnic group" is an anthropological category, not a biological one. The correct biological term is "subspecies", which Wikipedia defines as "populations that live in different areas and vary in size, shape, or other physical characteristics (morphology), but that can successfully interbreed."

Using “race” in a social context makes sense and is far from being racist.

Given the history of its usage in that context, I have to vehemently disagree. Plus it is so ill defined that it is a useless term anyway. From Wikipedia again: "[...] various definitions exist. Sometimes it is used to denote a level below that of subspecies, while at other times it is used as a synonym for subspecies."

Using it invokes all the Social Darwinism and whatnot that the Nazis and others abused it for. So where is the sense in using it exactly?

Using the term "race" as if that is a thing enables and facilitates racism and racist language. There is zero actual use for the concept among people who are not racists.

Much better :)

Haplogroups

Nope. Social constructs can only be made up by social people. Racism is inherently anti-social. Race is not a thing. There is no "race" of any kind of humans. Saying otherwise doesn't make it true, it only enables and facilitates racist language.