Does anybody have any experience on how to balance the input of a slightly different pairing...product manager and project manager?
Outside of those circumstances I have never seen any value in it. For software only initiatives the entire project management function is little more than ignoring Jira boards and calling meetings with lots of people to “check on status”.
If you have anyone doing this then your organization is in a bad place and needs to be set right, it will not get healthier.