My own observation is that it's more important for managers to be well-organized, remember details, and keep track of things
Not sure if that's what you mean by soft skills, but I generally think of soft skills as things like ability to communicate well, navigate conflict, and apply emotional intelligence to people management
The "soft skills" as I understand them are more important for roles like team lead/staff, whereas the organizational skills (and maybe even a willingness to be unlikeable at times) are more important for management.
That's why I think a lot of engineers prefer the IC track (I personally think my organizational skills and focus don't qualify me for management, although I enjoy being a lead)