Take this with a grain of salt, as I've never used PostCSS and had to look up what it even was.
Of course, as PostCSS is a tool that applies to .css files, there is no particular reason you need to reimplement it in Go to be able to use it with Go based serving; the Hugo Go framework apparently includes PostCSS integration of some sort:
https://andrewdavis.me/post/rewriting-my-personal-site-with-hugo/ has an example under the heading Integrated CSS Processing.
Given that, as I understand it, part of the appeal of PostCSS is the library of modules for it, and the fact that these modules are certainly not going to be compatible with a Go reimplementation, you may need to consider whether you use any modules and what would be involved in reimplementing their functionality before moving to a pure-Go solution.