Pronounced like “hope” without the “h”, it is indeed a local (Midwestern U.S.) "expression.
It is, mostly, a “shorthand apology”.
“Ope, just gonna squeeze right past you and grab the ranch” (dressing) or “Ope, grab the butter while you’re up whydoncha?”, or “Ope, I spose it’s about that time.”
In the context of that sticker, it’s more like a “sorry, not sorry” but less intense and more polite.