Ok I think the thing I missed was in
float3 lightVectorWS = -mul(float4(lightVector, 0), InverseView).xyz;
float depthInLS = getDepthInLS(float4(input.PositionVS, 1), lightVectorWS);
float shadowVSM = chebyshevUpperBound(depthInLS, lightVectorWS);
I was wondering how I could make my shadows work with my non linear depth and yours cold work too with the same maths.
To sample from the cubemap, isn't it enough to use texCUBE with the light direction vector (your lightVectorWS), instead of trying to find the transformation with getDepthInLS (LS= LightSpace right ?) Some tutorials says tit is not necessary to normalize the lightvector, some say to... I'm lost, maybe my shadows are working by chance...