Thanks for the response! One thing that may help - dealing with impoliteness is an expectation of a __people__ management role, but not an expectation I would have of project or product managers. If you’re consistently seeing PM burnout, it will only hurt your position to defend it by appealing to the manager name in their job title.
My experience is generally in environments where project managers are expected to also manage the people working on the project, at least to some extent, and so I didn't think to make this important distinction.