As an alternative "explanation," it sometimes seems to me that mirrorless cameras can miss critical focus on relatively low-contrast subjects. (Comments clearly worth less than 2 cents.)
This type of comment, whether or not is worth less than 2 cents, seems very relevant to this image.
The significant posted crop relative to the RAW image is a potential complication.
There is more feather detail about 4 inches in front of the eye than surrounding the eye.
If the intention was to focus on the eye - it is obvious with reasonable eyesight even within the limits of web image reproduction this did not happen with the posted crop
Cropping an image (which has happened) has a depth of field effect similar to getting closer to the subject.
As a starting point a long time ago when Nikon used to regularly produce a book of all their products, in the 1996-1998 edition they quoted 6.49 to 6.51 metres (less than 1 inch) depth of field for a 600mm at f4 at the then 6.5metres closest focus distance.
The two Z 600mm lenses can focus around 50% closer - with an expectation of one quarter of the depth of field at around 4 metre rather 6.5 metres.
This seems to me a good starting point assumption for this image crop - and helps explain the sharpness detail difference between the feathers around eye and the closer feather detail is a depth of field issue.
I speculate the image crop is close to about a 10 inch wide subject.
As a separate detail the Nikon specification for the 600mm f4 Z seems to indicate a subject width of 10.7 inches wide at MFD.
As this is a cropped image focussing closer than the MFD is eliminated.
In the RAW file image contrast seems relatively low and the birds eye is small in the frame.
While I was not there my speculation is subject conditions (contrast, subject size in the frame etc) were not enough for accurate AF on the eye.
IMO the still slight softness in the best feather detail in front of the eye is most likely due to the significant crop and is possibly also slightly limited by web reproduction limitations.
Depth of field sharpness in dof tables seems to be based on a historical 1/100 of an edge blur being just acceptable when the whole image area is included in a 10x8 inch print viewed at a "comfortable" viewing distance of about 15 inches.
On this basis your cropped image is distinctly sharper than the basic dof assumptions - so relatively well done - especially as few remember image resolution reduces in lower contrast lighting.
Sharper detail IMO is possible - but only when you can get closer to the bird, preferable in sunlight.