Many have commmented on Sara Taylor's alas, no longer remarkable views on oath-taking, but nobody, so far as I know, has called it out for what it is. Here's the transcript of Leahy and Taylor's exchange via Big Orange:

LEAHY: And then you said, I took an oath to the President, and I take that oath very seriously. Did you mean, perhaps, you took an oath to the Constitution?

TAYLOR: Uh, I, uh, yes, you're correct, I took an oath to the Constitution. Uh, but, what--

LEAHY: Did you take a second oath to the President?

TAYLOR: I did not. I--

LEAHY: So the answer was incorrect.

TAYLOR: The answer was incorrect.

LEAHY: No, the oath says that you take an oath to uphold and protect the Constitution of the United States. That is your paramount duty. I know that the President refers to the government being his government -- it's not. It's the government of the people of America. Your oath is not to uphold the President, nor is mine to uphold the Senate. My oath, like your oath, is to uphold the Constitution.

The idea that a civil servant takes an oath to the Leader has a name, and a history: