There seems to be a common misconception about the job of a Product Owner: Many people have the impression that the main job is backlog management.
None of these job requirements are technically incorrect: A product owner is in charge of the backlog. This is obviously the case on paper in the Scrum Guide, but also in real life.
Only if the Product Owner is actually doing product management, which is a very broad job, he or she is able to manage a backlog. It is only after a proper discovery process that the PM/PO is able to focus on the delivery area. In the words of the Double Diamond: Only after understanding the problem space can the PM/PO focus on the solution space.
I don't know why the job postings make the backlog the focus of what they're looking for. I can only imagine that hiring managers and recruiters have a very poor understanding of product management, reducing it to the mere management of open issues in the backlog.
One is companies that split the role between a product manager and a product owner. But be careful! These need to be two people who work very closely together and spend a lot of time in the same meeting talking to the same people. They both need access to customers, users and stakeholders, as well as engineers.