Witness stand oath is really just a formality. Lying on the stand is perjury. Actually doesn’t matter if you took the oath, it’s still perjury. In practice that oath is really just a person saying “yes I know there could be consequences”.
I think I’d take those words as a little more than formality.
Oath: I swear by Almighty God that I will tell the truth, the whole truth, and nothing but the truth.