I'm not sure about zero sharpening but I have the GH5, GH6 and S1, the GH6 is less "sharp" than the GH5 in 4K. There is far less artificial sharpening, even when I set the sharpness of the GH6 at +5, the GH5 at 0 is still sharper. However the Open Gate 5K of the GH5 is still beautiful, there is almost zero sharpening and noise reduction, the image is very "organic".
The issue I have with the GH6 is the new noise reduction algorithm (called 3D), it makes the low light really cleaner than GH5 but it also smear details in some areas of the image in low light even at ISO 200 (a bit like the Samsung NX1 but much less aggressive), even with the NR set at -5. I think there is no miracle, we speak about a M43 25MP sensor so some concessions must be made, but I was very surprised to see the GH5 retaining better details (the trade off is the noise).
The 5,7K is a different beast, it uses more sharpening and a bit less noise reduction (the footage is sharper than the 5,9K and 6K of the S1), however there is a little crop in this mode and nobody speaks about it.
For me the big advantages of the GH6 are the new color science, the 4K 120fps and the very good stabilization making (almost) possible handheld walking video.