I've found it incredibly helpful to include the user experience design as a part of refinement. I've also found it helpful to consider UX design as part of the product management organization.
Discovery is not only discovering the requirements that stakeholders have for a system, but also how the stakeholders best interact with the system. Although your product managers tend to know about the domain and the different stakeholder classes and how these people intend to use a system, understanding user experience design, user interaction, and user interface design principles are a specialty.
Some of the work is common between requirements engineering and user experience design, such as identifying personas or user classes and creating user flows and user stories or scenarios. However, user experience design uses this to create wireframes and other mockups or prototypes and conducts various tests on what the right interactions are for the different users. The output of these tests is used to refine the criteria used by a development team to build the product.
This does not mean that your UX designers can't operate within a iteration cadence, just like the development team. In fact, it may be beneficial to have them operating on a similar cadence. However, the work that they are doing is actually discovery for future work to be developed by the team in later sprints.
There's also the case where you don't have a dedicated resources for UX/UI design work. In this case, you should consider the design work to be part of whatever backlog refinement activities you have. Frameworks, such as Scrum, provide guidance on how much effort should be allocated to backlog refinement. Some of this time can be the team reviewing, estimating, and decomposing the work while some of this time is used to support product management in the initial development of the requirements, which would include designing the UI and any kind of user testing against the design and mockups.
If you need more than the allocated time for refinement, you should plan this work as part of the iteration. Ensure that you have specific work with specific deliverables laid out so that way the team can estimate the effort per the team's process and plan it accordingly. But do consider that these design tasks would need to be done at least an iteration or two before the implementation deliverable work to allow the designs to be used to inform the estimation and refinement of the work to implement the design,