good news: https://ibb.co/khWxmwg

make the same node setup in both hair textures including the transparent one
also take notice of the bottom right corner where the blend mode is alpha hashed

I basically just re created the hair in blender with their own particle system so your not entriely late since I never found a permanent resolution, but if theres any way for blender to mimic the way source handles this kind of hair would be g r e a t l y appriciated!

Im a little bit late here, whats happening here is very common and I don't believe that there is a "proper fix" for it. Its just how source exports hair into Blender, or how valve (and pretty much everyone else) makes their hair in Source