According to the Srcum in Agile for Enterprise, I understood that the PO was a just Role in the Squad, Not a Leader. But In the your explanation, PO looks like a top level of leader in the organization. I wonder what is different between startups and enterprise company's PO?
I disagree with what you define as a Product Owner. You've listed multiple sets of responsibilities of different jobs within a team. According to you, the Product Owner is not only the Product Owner, but also the UX Designer, Project Manager, Scrum Master, Product Tester, Mind Reader, Backlog sorter and an Oracle. The problem with a one-man band is that they don't quite sound as good as a band playing together. A more accurate analogy would be that the Product Owner is more of a conductor for an orchestra. Their job is to put on a good show for the all people who paid $200 for their tickets.
I prefer to use an analogy of a kitchen where the product owner is the head chef responsible for the the creative direction/vision of the menu and the approver/gatekeep of quality or 'done'
Before becoming a product owner, you need to know product design, uiux design, marketing research and more. If you do not have these, what you will do is just like a "Projct Leader", nor a "Product Owner".
I think whether a Product owner fulfils these responsibilities themself, or coordinates other people fulfilling these roles is very much dependent on the size of the team, the size of the company and the type of product being worked on. In a very enterprise situation, all of these responsibilities may be fulfilled by separate people. Meaning the product owner needs to coordinate input from various stakeholders and work from various employees. In a more start-up environment, an R&D project or small team situation, it may not be appropriate to hire people for all of these roles. The product owner can act as the decision maker for these responsibilities, to ensure the project continues to make progress.