What I'm noting is that both images are back lit.
When your subject is back lit, in the way they are, you get softness because of ambient light. Light is being reflected from many sources at many angles. You can probably solve the issues in the shots you've posted, especially the dog with a bit of fill light. The serious birders where I live have very powerful flashes mounted to the tops of their lenses with telephoto attachments.
If you don't have good light on the subject there's nothing you can do. You don't have bright enough light to create contrast and contrast does more to create photographic Sharpness than anything else. When you are back lit, you need to over-expose not under-expose. You probably missed by 1.5-3 stops.
I'm not seeing a problem other than that.
From yesterday....
K-3 and DA 55-300 PLM at 150mm
ƒ5.6, ISO 200, 1/2000s
There were 6 shots in this sequence, I threw 5 away, they were reasonably identical. IN other sequences I was able to pick out the best image and toss those not as sharp. I always shoot 3-6 shot bursts, when shooting moving critters or critters that might move, but depending on circumstances as much a 23 shots filling the buffer.
Also notice where the shadow is. It's on an angle to the bird's leg. That kind of lighting offset also creates more contrast, by creating a small shadow outlining the feather detail. So also important is the angle the light is hitting the subject. Head on is usually not the best. The owl is tough of course. It is where it is.
I'm advising ignoring everything else said so far and concentrate on better light for a bit. Pentax's are very good with stationary objects shooting from a tripod. IN body SR requires a little more tolerance for missed images than SR in the lens, you really have to keep the camera stable just to achieve focus. The in lens SR makes focussing easier. But, I compensate by taking 3-6 image. One of them will be good.
If you have good crisp light and are still missing shots, we'll talk further.
P.S. Also make sure you are set to focus priority, not shutter priority. On that first shot of the owl, your shutter shouldn't have fired.