The Cardinal image appears to be focused on the rocks behind the bird and shows pretty classic motion blur on the bird itself. That's not a noise issue, that's really more of a focusing and motion blur issue. The Starling image was clearly shot in a lot more light given the smaller aperture (/6.3 vs f/5.6) and the much higher shutter speed (1/3200" vs 1/320").
Based on these two images I'd say you ran into camera and or subject motion issues in the slower shutter speed shot and possibly back focused a bit on the rocks but what that image shows is blur and or focusing issues and not classic noise issues. Noise shows up first in out of focus background areas and usually not so much on the primary subject itself unless it's really bad.
A high resolution camera like your Z7 or a D850 will reveal technical issues much more than lower resolution cameras so things like motion blur tend to be a lot more apparent than they might be on other cameras with lower resolution sensors. Unless you have other examples that show more noise in similar out of focus areas I'd say you're seeing motion blur issues at lower shutter speeds which would be completely normal.