And there likely isn't any sort of "oath" at all related to any polygraph. The poly isn't about signing agreements, it's about truthfully answering questions. The scope of the questions is different depending upon the agency and the clearance. The NYT is not an unbiased source. To quote the article:

"In interviews and polygraph tests, the F.B.I. has asked senior employees whether they have said anything negative about Mr. Patel, according to two people with knowledge of the questions and others familiar with similar accounts."

So this can be true and misleading at the same time. Some of the questions asked relate to social media activities and posts related to classified work. I can imagine a scenario where answering these questions would lead to a discussion about Kash Patel. Having a poor opinion of your boss while working in a classified environment could make a person more prone to leaking sensitive information. The FBI has been leaking like a sieve lately.