So here’s Suzanne with some points scattered on her head using Distribute Points on Faces. Can I tell a shader where those points are and have it draw soft circles at those spots (with a size/falloff that matches the size/radius of those scattered points)?
I dont know about geometry node but you can use ambient occlusion node and add colorramp for making soft gradient around intersecting object. for eevee you have to enable the ambient occlusion in the render properties.you can use the distance or colorramp for the distance
Well your underlying problem is that geometry nodes works on geometry level. So you will need a really high mesh density to transfer it to the shader with a suffiicient quality.