That last part about managing stakeholders' competing interests and expectations might be the most important part. As an engineer, I have been furious with bad

That last part about managing stakeholders' competing interests and expectations might be the most important part. As an engineer, I have been furious with bad product management pushing near impossible designs and setting ridiculous deadlines without consultation in the past. If I had to hire for a product manager, an indication of the skills associated with this would be what I would look for. Critical thinking and diplomacy are crucial skills, in addition to all the things you have mentioned.