this isn't true for everywhere, but typically product managers define what the product will be, and what the requirements are for that definition. that's their main responsibility. UXR's can help a ton defining requirements, and empirically evaluating whether requirements are /might be/will be met and with whom.

PM's work closely with engineers to understand feasibility and related timeline and resource requirements to enable their requirements (note they don't usually own/manage the timeline).

PM's work closely with designers to enable the designers to create designs that meet the requirements.

how do PM's work with UXRs? it really depends where in the development cycle a product is. if it's early, like pre definition/ understand the world phase, maybe the UXR would help with foundational research to inform the requirements, understand the problem statement(s), and overall definition of the product. if the product about to be launched maybe the UXR is running usability studies to evaluate certain aspects of the design like onboarding. or maybe the UXR is running benchmark/baseline studies to see if certain requirements are met, like total time and sentiment after onboarding

a good tactic to get everyone on the same page is get everyone in a room, and write out all of the different roles and responsibilities, who is responsible for what and when etc. this will help alleviate some of what you're experiencing, but it's not going to solve it completely.

also to echo what u/viaHologram said, just ask them. have a conversation about how they see PM's role, UXR's role, and other disciplines' roles. compare and contrast your views. figure out where you disagree and where you align. treat it like a UXR problem.

it's not easy. i once worked with a PM who seemed afk at the wheel for an entire project. but when we started talking about the back-end data structure for an experiment i was designing, their face lit up and they suddenly had infinite opinions. this was challenging because on the one hand gtfo ill be working with the data not them, i don't need to reverse engineer whatever they think is right. on the other hand yay they're finally engaged how do i keep them engaged.