Sony a7III photos coming out very soft

This is not screenshots, but full resolution jpgs, 6000 x 4000.

Click on the images, then right click and choose Open image in new tab. Then click the image (magnifier cursor) to view at 100%.

These images look perfectly normal to me. Unsharpened raw files are always a bit soft.

You may want to use the Masking slider when doing sharpening, which will protect noise in flat areas from sharpening.

Hold down the Alt key to see the effect. White areas will be sharpened, black areas will be protected.

To add: you must view at 100% (1:1) or greater in Develop module. That one module uses a unique preview architecture and provides the most accurate preview of the image and the current settings.

What exactly are we comparing in these two sets?

To properly judge sharpness, you have to view at 100%. This maps exactly one image pixel to exactly one screen pixel. Any other zoom ratio and you get screen resampling and inevitable softening.

Then adjust sharpening to taste.

That said, zoom lenses are usually slightly softer than primes. It should be sharp center (even at 2.8), but sharpness falls off very rapidly off-center. Ideal aperture is 2-3 stops down.

Sigma is generally very good optically, but autofocus is always the weak spot with third-party lenses. This is proprietary technology, and third-party manufacturers have to reverse-engineer autofocus. I have one Sigma lens that struggles a bit with getting proper focus. It's slightly off very often.

If you want an absolute reference lens to judge sharpness against, I can recommend the Sony/Zeiss FE 35mm/2.8 ZA. It's not too expensive and very handy, and yet so sharp it will bring out everything the sensor is capable of. I use it on my a7rIII, and it's still my favorite lens.