Different lenses have different performances at different focus distances.
For example, a lens designed for portraiture may perform vastly superior wide open when shot closer to it's minimum focus distance as opposed to at infinity. This isn't something I've actually experimented much with on the K1 with the Pentax 24-70. Generally speaking I've been very very happy with mine. It's as sharp as any other pro grade 24-70 out there. Probably better than most in the sense that you benefit from IBIS.
Another thing to try.... as you are testing on a tripod, have you considered disabling the shake reduction system?
Also try with live view to confirm if it's simply a case that you have a soft copy.
I've had the pleasure of trying two different 24-70's on two different K1's. Tack sharp at the point of focus wide open. Relative to most other pro grade 24-70's out there it's up there with the Canon L 24-70.
I'd be surprised if the PDAF needed much adjustment as the glass doesn't really suffer much spherical aberrations which can play havoc with PDAF on DSLR's. Possibly +/-2.
However keep in mind that (with your portrait sample) F2.8 is still a very narrow DOF so the suggestions about focus adjust are good to get critical focus.
I've also tried the 28-105 and that is a beautiful lens. However from a sharpness perspective the 24-70 is producing sharper results wide open that match what I've seen from the 28-105 at F4. In my mind it's no doubt the superior optic.
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