Getting closer is not always advisable but the 800 also does not overcome atmospheric distortion.
I have had the 800 pf since 5-1-22. I have photographers ask about it because they are having trouble getting "in focus" photos of birds accross a lake etc. with 300, 400, 500 to 600mm focal lenghts. I first alert them about atmospheric distortion not being overcome by the 800mm. Some have shared their images and it is seldom a focus issue but is an atmospheric distortion issue. So first I tell them about atmospheric distortion that is present any time there is a temperature variation between the air you are shooting through and the surface of water (frozen or liquid) or land you are shooting accross. As that temp differential gets larger and/or the distances get greater the impact gets more dramatic.
Unlike Thom whose wildlife photography is mostly mammals from a safari vehicle. I am a run and gun on foot bird photographer with subjects in a wide range of weather, distances, terrain, habitat, sitting, hiding in the brush, running and flying. I am a citizen scientist and search for and photograph a lot of very small birds like sparrows and gnatcatchers and larger like eagles, geese and swans. I hand hold and do not use blinds/hides.
One strong caveat I have about trying to get closer. There are many times it is better that you do not try to get closer to avoid disturbing the animal's hunting, causing nest abandonment or disclosure to predators etc.. No photograph is worth harming the subject by depriving them of food, stressing to the point of exhaustion or exposing them unduly to predators. In those cases the 800mm really shines and I frequently have the Z9 in DX mode so 1200mm equivalent FOV to be able to stay further away.
I have a 1.4TC and carry it sometimes but have not used it on the 800 pf except for tests. Since my subjects and I are on the move and one second I might be shooting a sparrow in the brush at close to minimum focus distance and suddenly a hawk or falcon flys by or vice versa, there is no time to add or subtract a TC and frequently barely enough time to push one button on my lens to toggle between dx or fx mode.