The more I think about it the more I think it’s actually something I say, just not consciously. And I’m from the Mid-Atlantic; not the Midwest.
Also found this article that hypothesizes a few origins including, yes, a shortening of “oops!”
No. It is very specifically pronounced “Ope”, like “hope” without the “h”, and it has it’s own distinct meaning.
The thing I’ll say is closer to “‘up” And I use it more like “oh no! You caught me inconveniencing you. I’m so embarrassed 🫣”
Definitely seems related though…