It involves a similar skillset. Especially if you see soft skills as something an IC should be capable of then you should basically have everything you need to be dumped into an EM role as an IC. If you don't the overlap is still quite substantial. And the companies of the world generally agree with the view that similar skillsets apply - that is why they keep promoting software engineers to be engineering managers. If the skills were different they'd promote more socially savvy individuals than you generally find in engineering.

For an IC the application of those skills will be quite novel. But that is what career progression is. Same skills, new puzzle.