If you're trying to separate "face to face" performance and put that in the domain of HR, and "technical test" performance and put that in the domain of the technologists, then you're going to have a bad time. That prospective hire who did great on the face to face isn't going to spend part of every work day chatting with HR...

Between your technical people and your technical management, there should be enough people skills to function coherently and effectively as a team. As such, those people together should have enough people skills to figure out whether a prospective candidate has the people skills to function effectively in the team. If those people see people skills as exclusively the domain of HR, well then you made prior mistakes in hiring that cannot be remedied with further mistakes.

This is exactly the sort of mission confusion that results in HR departments overreaching. If HR sees itself as "the people people" and its role as evaluating candidates for "people skills" and engineering's role as evaluating candidates for "technical skills" that's an unworkable division of labor and will invite improper encroachment from HR into the hiring process.