That's kind of beside the point - for the sake of argument, let's say managers only care about "budgets, timelines". It would still be a stretch to switch from an IC role to suddenly managing the "budgets, timelines" not only of a team but of a whole department
I am convinced, that the guys, who got promoted, know how to manage things. Even in toxic place I worked as an important IC I assisted doing project plans and technology roadmaps. The department things were same charts, but without technical slang and absolutely anonymized threading workers as an abstract number “headcount”.