Are we talking about product managers or project managers? Those are completely different things. As far as I'm aware the tech giants have TPMs (Technical Program Managers) for very large cross-cutting efforts but mostly have engineers do their own project management. The PM discipline is about coming up with products and working out their details between all the stakeholders. They're not running the agile ceremonies. They're getting the copy signed off legal and working up an experiment plan with data science to choose between design's three different mockups.