Generally speaking, the advice I gave in a previous question holds - one software product is represented by one Jira project. In the simplest case, the definition would be the product manager defining changes by writing some of the tickets in Jira, the UX designer linking tickets to aspects of the mockup, refinement with the entire team, and the use of the Jira Components field to identify iOS vs API work.
However, I can see cases where you may want to isolate the product into a Jira project. Often, this can be more useful where you have a complex product or a portfolio of products that need to be aligned. The output of the product management organization could be things like specific changes for multiple products in the portfolio, design guidelines, component libraries. In these cases, the software product would be different than the product management product and services.
At this level, the biggest factor is your organization. Consider the size of the different departments involved, the existence of product lines or product families or product portfolios, and the products or services offered by each team to other parts of the organization.