Perjury is lying under oath. The statement must be made under oath to be eligible for perjury. And making a statement under oath is a formal process, dictated by court or law.
You cannot make yourself be under oath. Swearing something to be true doesn't count, unless there is a legal context that makes it true. Swearing in a witness in court makes that happen. Some laws (like DMCA) make statements in certain documents oathful. But it is the law, not the document, that decides that.
In my common law country, at least, when you swear something, it's an oath, and only an oath. We have a non-religious variant, no almighty God required, where you solemnly affirm to the same effect, and false information provided is perjury, punishable by up to 7 years imprisonment (if you perjured yourself in a judicial proceeding), unless you perjured yourself to get someone falsely convicted for a serious crime, then it's up to 14 years.
We also do statutory declarations, where you only declare it to true, but false information in one of those is still a crime, with a lesser penalty.
Oh, and we have a fun wee clause that maybe your jurisdiction doesn't? Where if you swear an oath, it can still be perjury even if it's not being sworn in a judicial proceeding. Only 5 years though.
So yeah, what does "swear" actually mean in the US? I don't get how you'd swear a DMCA takedown without your oath being taken. I figured if it was legit sworn, they'd do the usual "sworn this day X at BLA, witnessed/authorised/etc by Z"
Are they just trying to sound legal and scary, or is that format required in a takedown?
Not a lawyer, nor do I play one on TV, but I've been an occasional customer of the judiciary sufficiently to pick up the vagaries.
Sigh.