At least for California, you have to look for the California Olive Oil Council seal if you want to be sure:
https://cooc.com/about-the-seal/
For example: there is a company called "California Olive Ranch." It used to have a popular olive oil sold in a lot of larger grocery stores that had the COOC seal. Then it started to source olives (oil?) from somewhere outside California and blend with the California olives[1]. That broke the rules of the COOC seal-- to have the word "California" on the label you can't blend with non-Californian olives. So the seal is no longer on that bottle, but the name "California Olive Ranch" is obviously on that label because it's the name of the company.
Thus, a shopper would be misled by your second sentence and buy an oil with olives and whatever else from imported non-Californian sources. That means the third sentence is also wrong-- looking for harvest dates and COOC seal isn't something that the shopper can do to double check their choice. Rather, that is the only thing they can do to be sure they're getting actual virgin olive oil of sufficient quality (the seal) that isn't rancid (the harvest date being within less than a year).
Edit: I don't have a link, but there was a recent COOC fiasco where a lot of the smaller farms got up in arms due to a proposed language change in the requirements for obtaining the seal. Don't remember the details, but it sure sounded like it would have made it easier for a member to blend with some amount of imported olives and still carry the seal.
Honestly, I think there's enough intrigue and drama in this topic of finding bona fide olive oil to start a substack subscription thingy if anyone is interested in that. :)