As someone who used to wonder about this I think I've finally cracked the code.
Biggest factor for me is that it pays to shoot primes. That works both from the pocket perspective and the results perspective. I have a Sigma 150-600mm Sport and it's plenty sharp, but when I bought the 300mm f4 PF my head exploded from the first image. It really is sharper. I now shoot with a pair of D500's, one with the 300mm and one with the 500mm f5.6 PF. For years I told myself I could never spend the money, and I get that not everyone can, but after shooting with them I cannot go back. It is a huge factor in sharpness and OOF quality. And with the D500's having 10fps and a super focus system means a lot.
Next is shutter speed. High ISO is not your friend when you have little birds, but movement blur means that you probably ditch the shot, so better to have a sharp shot with noise than no shot. I'm almost never under 1/1600s any more. When they're sitting on a branch it doesn't matter, but when they jump during a burst it's the one that got away because it's blurring that you always want. If I can shoot at 1/2500 I'm there, which I usually can on a sunny day.
Finally it's all in post processing. I used to jump through hoops to find detail in my shots, but some of the new software is just too good not to use. I've reduced my workflow to this:
1. Import and crop in Lightroom. No edits other than an applied camera profile and lens correction; no noise reduction or sharpening. Then it's sent to Photoshop.
2. First step is to use Topaz Denoise AI. This both reduces noise
and sharpens, but it does both selectively which means that the noise gets reduced without reducing details.
3. I
now open it in Camera Raw Filter from within Photoshop and do all my light adjustments to the denoised image. I can take images that are -3EV from perfect exposure and bring them to life
without adding noise. I do all the edits here that I used to do in Lightroom.
4. Now I apply any other corrections I would do in a normal Photoshop session. Remove unwanted objects (sometimes I do this before Camera Raw), dodge, burn, selective color adjustments, background blurring, etc.
5. I send it to Topaz Adjust AI which has separate Clarity (by luminosity level) and Detail (small, medium, large, and sharpen) sections. Here is where the image pops. In general I will only use the Detail and Sharpening sections, increasing the small details slightly (while decreasing the "boost" slider), and then boosting the medium details until it looks right. Then I'll notch up the sharpness slider if I think it needs it making sure I don't add halos. (Note: It has other sections that mimic some Camera Raw functions, and I guess it's meant to replace that function in the "Topaz Studio", but I find them to be less effective than ACR.)
6. I now stare at it and see if it needs anything. If I have a little haloing I use the blur tool on image edges. I might dodge and burn some more. And I might sent it back to Camera Raw to add vignetting.
That's it. My bird photos are better than they've ever been. Feel free to judge for yourself on my
Instagram page.