This obviously varies from role to role but I was told I would be highly involved in deciding what the team does and how they go about it. The reality is that I am responsible for arbitrating the delivery of decisions from more senior managers to the teams and the decisions from the teams on how they execute on those decisions back to the managers.
Facilitating the growth of other engineers is wonderful but, frankly, I can do that (and was doing that) as an IC.
If I'm honest I don't think the exact role I want exists out there but I think I'll make a far better "lieutenant" to a manager who actually likes the job than I make a manager who is becoming increasingly unengaged with their own role.
"What would you say... you do here?"
Either the person quits.
Or the person resigns to giving mediocre output and coasts.
Neither is good for the business and yet people keep pushing workers (not even just in tech) into that position to the point it's now a cliché.