I agree with this generally for TPM and project managers. Even then it’s not that they truly do no work, but that the core coordination work they do (which requires very few, but no 0, man hours) could be done with higher fidelity and context by an EM without it really adding much more work to an EM’s job.

Engineering managers are responsible for their team’s output; they are often held responsible when their team fails to deliver. Product Managers are responsible for setting and prioritizing the product roadmap across a lot of stakeholders, often with specific business goals to achieve, and spending a lot of time doing stuff like talking to customers and helping with marketing/sales/planning/etc; they are also often held responsible when they don’t deliver on these tasks.

It is a very junior engineer perspective to consider it not actual work or for them to have no real responsibilities just because they are not coding. In my experience it has also been common for EMs to be at least staff level ICs skill-wise and PMs to have enough software skills (often having previously been SWEs) that they could be SWEs if they preferred that.