How to get a nice shadow pass

Hi everyone,
I got a problem with my shadow pass that not correspond to my combined image lighting. How can I get a smooth shadow pass corresponding my combined image ?
Have a nice day !

Combined image :

Shadows pass :

Comparison in After Effects (shadows pass tint in red) :

This is not a 100% correct physical explanation, but think the shadow pass shows you the boorder between light and darkness in parts sharp or smoother. But depending on the material and the interaction between light reflecting objects the part in shadow can reflect a bit more light than the pure shadow. The light in the shadow can be different because of the different normals in that bend area and the different light source positions or even hdri but the shadow pass is only grayscale (1-dim); normals are rgb (3-dim).
So, you maybe have to blur the shadow pass a bit ? Depends on what you wanna archive.

Thank you for your reply. I’m trying to export a light pass for use in After Effects to recreate the combined image with separate layers. I think I’ll render the lighting separately, with a white shader. I’m endering with Eevee, without HDRI. I’m new to Blender and at the moment I’m a little disappointed with the way Blender is handling passes.