There are two answers here - the Scrum answer and the my practical answer.
In Scrum, there are three "accountabilities" (prior to the November 2020 revision, roles) on a Scrum Team - Scrum Master, Product Owner, and Developer. A team has one Scrum Master, one Product Owner, and everyone fits into one of these buckets. However, if there are multiple teams working on a single product, the Product Owner would be aligned with the product and shared across all of the teams. Based on your description, it sounds like the Business Analyst's work and the things that the Product Owner tend to do have a lot of overlap, however the BA isn't in a position to have their decisions respected by the organization and someone else is ultimately accountable for the decisions regarding product direction.
Based on the definition in Scrum, I believe that Scrum vastly underestimates the amount of effort required for product management and discovery.
The Scrum Guide says that the "Product Owner is one person, not a committee". Given the nature of product management and the vast scope - market analysis, competition analysis, business analysis, requirements engineering, commercialization, sales, scheduling, budgeting, and more - I don't believe that it's reasonable to expect one person to be able to handle this. This is compounded when you consider human factors and user experience as a part of product management. The idea that there should be a singular voice making product decisions is sound, this person needs to be supported by a variety of people that, together, have all of the skills necessary to carry out product management.
Business analysis is one of the skills that may be necessary to support a Product Owner. This could be a specialist individual or it could be someone who performs business analysis along other work.
Once you realize that there is a team performing discovery work, you can look at dual-track agile (1, 2, 3), where the discovery work feeds into the Product Backlog for the Scrum Team. There isn't a hard wall or hand-off between the two teams, there has to be collaboration to make sure that both aspects are doing the right thing. However, there's a clear distinction between understanding and defining the problem (discovery) and delivery (technical understanding and definition, prototyping, design, implementation, test, and deployment).
The team behind the Product Owner becomes the source for answers to questions that the developers have. This could be the Product Owner, or the Product Owner could defer to one of the specialists supporting the product.