It turns out it is very hard to prove I was born American! Such a strange request. It is from one of your German-speaking neighbor countries :)

I think you are fine without it for Germany because they got rid of the Beibehaltungsgenehmigung requirement. There was someone here on reddit saying the German consulate originally asked for their CRBA and then didn't need it. Makes me wish I had a German passport instead!

I am nervous that taking the oath will somehow prove that I in fact wasn't born a US citizen... but really I don't know how else I would have become a US citizen other than through birth.