Question Convert normal bump from object space to tangent space?

Hi there,

I'm trying to convert a normal map (object space) to tangent space in the shader graph with the Transform node, to be used in the HDRP Lit master shader. I don't know what's wrong but the result is a mess (flipped normals etc...). However, when I put the normal map in a HDRP Lit material, with the option OS normals, it works fine. Any idea of what's wrong here?