Thanks for posting, it's fun to see others' no flash, in the dark or twilight efforts. On the owl photo, I actually think if the image was less bright, it would reduce the perception of the noise, and show that this is not a daytime shot. At least I assume it wasn't due to needing the high iso.
Your owl was on the hunt and realized it was being watched. It was night and I think letting the viewer know this might make the image more interesting. By being as bright as day, the perception is that the image
should be sharper, but recognizing that it's a night shot gives the viewer a "window" into the owl's world, and personality. Certainly darkening the background might help.
I really like looking for night opportunities for nightjars and owls. Poorwills (thanks to @jhallettbbc for posting) are particularly fun because their tendency is to freeze when they feel threatened. I've had good luck with handheld flashlights or headlights, and no flash, but that means high iso. In fact, in my experience, I have to find them with a flashlight (look for the gleaming eyes), then do a slow careful approach (10-15 mins or more), keeping the light on them. If I use a flash, it's a one-time shot, they disappear after that photo. So, high iso is what I get. Finding nightjars in the day is really a challenge. I've only succeeded a couple of times.
My 300mm f/4 PF is what I'm trying now instead of my 500mm f/5.6 PF, to reduce the iso. Cold nights are harder as there are fewer insects out.
Here's a few shots in separate threads:
https://bcgforums.com/threads/learning-low-light-technique-with-a-d500.27249/ and
https://bcgforums.com/threads/common-poorwill-project-cont.28699/. (I haven't yet revisited editing of these.) All were handheld.
regards, Alan