I think they are very nice images, excellent color, and detail. I don't really see any difference between the focus of the tail and the head - may just be my skill in assessing images - both look quite sharp to me.
The first shot has a blurry tail and lower back. Initially I thought it was because I focused near the bird head instead of at the body center, but now I'm more inclined to WPMChan's opinion that the bird tail has motion blur.
The second shot has both a sharp head and tail, but the head is not as sharp as that in the first shot. I'm almost sure this is a motion blur problem. The head is not as sharp as some of my finest shots.
What I did notice in both was noise - looking at the images at 100%. At more normal sizes its not noticeable. I've found using DeNoise sometimes something I think it is a little soft or out of focus will become sharper using the DeNooise.
About noise: The second shot happened to use -1.0EV while the first was -0.3EV because I used a [-1.0, -1.7, -0.3] exposure bracket to prevent white neck overexposure. So, the second shot has more noise than the first if we use Active D-Lighting in NX Studio to brighten them up to the same brightness level.
It's also important to note that if you use Shadow Protection instead of Active D-Lighting to brighten up dark parts, Shadow Protection will result in less noise. This is because Active D-Lighting adds or keeps more contrast, and more contrast leads to more noise.
Highlight Protection and Shadow Protection may be used to prevent the white neck from overexposure and to recover more detail on the white neck. Professional photographers would tell you a photo should never has a plain white portion (with the exception of the sun).
I'd be happy to put one or both of them through Topaz DeNoise if you'd like?
Here is the Google Drive link for the RAW for you RAW and post-processing junkies
https://drive.google.com/drive/folders/14v3k6FfOHrQ8djyzyoyMTUVqu4b08Iw8?usp=share_link
Again, very nice images - sometimes at least for me better not to nit-pik the images.
Ev
I don't know about you, but as far as I can tell when you repost images here there is always some degree of compression - the image on your PC will look a little different when posted here. Or it can look a bit different.
The file on goggle drive is not the RAW file - it was a JPG.
I reduced the noise first - I think there is a clear difference. One of the best things I've done is invest in noise reduction software - user friendly. I'm a beginner only had it a couple of months.
Editing - the only thing I did to it was fix the small amount of blown out white on the neck. The white on the chin was not blown out.
After a sleep.
At first I thought you were wrong about the use of "chin", but now I found this image with Google:
Looks like a bird chin is quite different from a human's...
My processing methods/steps is to hopefully do as little as possible - this one as noted before looked fine, except for the noise. I didn't see the blown out white with my eye - the software ID'd it and I could turn the highlights down on just that small patch of white on the neck. My software is Luminar Neo - not as sophisticated and high end as some such as DXO, Photoshop, etc. But then again I'm not convinced I'm getting the best out of Neo yet.
Ev
Great result! Noise does seem to cease without a sense of loss of detail in hairs.
Thank you BC - don't know how I didn't see that RAW file in your GD. I went ahead an processed it - again I didn't do much, didn't need hardly anything according to my eyes. Those that are much more skilled at photo processing might have reason to nit-pik - I have no idea.
My processing is to keep it as simple as possible, as realistic as I recall seeing the bird/wildlife. Its a constant learning for me, which is fine.
Anyway - my software recognized your P1000 and I could choose a Camera Profile - chose Camera Neutral. No cropping, all changes were small increments - + exposure a little more and shadows, -highlights to remove the almost unseen blown white on the neck. Adjusted White Balance overall with the eye-dropper only. Masked the bird and added slightly small details. Used what's called the Accent Ai Tool, slightly - an all-in adjustment slider - that can substitute for many traditional controls, including shadows, highlights, contrast, tone, saturation, exposure, and details.
I did the Noise Reduction at the end. Topaz DeNoise provides 4 models of noise reduction - you choose the one you think (can be quite subjective) is best, and sometime tweek from there. I only tweeked as I recall Sharpness - more sharpness can introduce more noise. Increased the NR some from what the Ai model provided. So just a few clicks. I don't know that it's any better than any of yours, except for the noise reduction.
Also not easy to edit when you haven't actually seen the bird in person in the particular light it was in.
View in Original Size for best viewing.
Ev
PS As far as the "chin" - bird topography can get awfully detailed when ID'ing different part of a bird in particular all the different types and location of feathers.