Product Management Sets the Vision
Product management, and specifically the Product Owner role in frameworks like Scrum, are primarily about managing the vision for a product. The day-to-day work of product management involves a lot of things such as:
- stakeholder management
- market and business analysis
- product positioning
- prioritization of features and product backlogs
- direct or indirect budget allocations and release planning
However, none of these things should be the raison d'être for the role. Instead, an effective Product Owner should generally focus on collaborating with stakeholders, customers, and the development team to outline what should be done to deliver business value, and leave how to deliver that value to those who will actually be doing the work.
Traditional product management and agile Product Owner roles (whether Scrum, SAFe, or just "agile") do differ in scope and intent, so you won't really find a one-size-fits-all job description that works across all organizations. In all cases, though, UX design is a skill or product development activity that supports product/market fit; while there is some overlap, it should definitely not be confused with defining the vision for the product.
Some General Demarcations
For this particular role, you've already been told that "UX" (whatever that means to the client) is out of scope. Your best bet is really to ask them what they think UX means, and then avoid those things.
In general, though, a good user story map (which is often different from an interface-oriented user journey) should include what a user wants to do, not how they do it. With that in mind, some general demarcations between product vision and design would exclude:
- wire-frames and mock-ups
- graphics design and renderings
- implementation-level details about the product
- anything else that is a deliverable rather than a milestone, or an opportunity for feedback and validated learning
As just one example, the product development process might include an activity such as A/B testing of packaging, but the details of the packaging itself are not usually part of a predefined vision. Perhaps more importantly for your exercise, such details are not typically in scope for a user journey, because they aren't really things an end-user does.
If you find yourself focusing on how rather than what, you've probably crossed the demarcation. I'd strongly recommend that you focus on defining the general activities and outcomes you need to make a market fit, and leave all implementation details to the product development process.