What’s your working color space in AE? Pngs are 8 bit, so if your AE work is being done in 16 or 32, you will lose info no matter what. Try exporting with higher quality formats that support alpha channels and more than 8 bpc. For instance, tiff, exr, prores 4444, etc.
Also, if your shadows in-comp have blending modes, you will need to export them separately with the blending mode set to “normal”, and then adjust the blending mode within premiere