Although the Scrum Guide does say that "the Product Owner is one person, not a committee", it doesn't say that there can't be a team supporting the Product Owner. There would be a single individual ultimately accountable for Product Backlog management, in some cases, such as a complex product or a product with a large number of stakeholders, nothing prevents the organization from having additional product managers to work with the Product Owner. In fact, the Scrum Guide even says that the "Product Owner may do" Product Backlog management "or may delegate the responsibility to others".
One problem, and the smallest of them, is calling everyone a Product Owner. Within the Scrum framework, a product has 1 Product Owner and 1 Product Backlog. It would be inconsistent to have multiple Product Owners. Perhaps these other people could have different role names to make it more clear what they are responsible for.
If you have a lot of cross-team dependencies after migrating into stream-aligned teams, you may need to evaluate your architecture. That could be your product architecture or your team architecture. Perhaps you need to introduce subsystem or platform teams to handle certain cross-cutting parts of your system. Perhaps the architecture of the product isn't segmented into clear boundaries. It's unclear, but there are likely ways to reduce the dependencies, either through organizational changes or product changes.