I’ve photographed bald eagles along the Mississippi in winter — soaring and diving to the water surface for fish — with my Z 800 mm PF, both with the bare lens and with the Z 1.4x TC. Handheld. No issues tracking the eagles. Of course they are not the fastest or most erratic flyers.
I’ve also photographed great blue herons, great egrets, double crested cormorants, Canada geese, and various ducks in flight along a different stretch of the Mississippi in the spring with the 800 mm PF, with and without the 1.4x TC. Again worked great. Generally closer than the eagles I mentioned.
In both cases, using a Z9. Happy with the results when I want more focal length. Of course, you lose a stop of aperture. Beyond that, the only issue was, with the TC, it meant sometimes I had too much focal length. And you can’t change an external TC quickly as you could with an internal TC on a Z 400 TC or Z 600 TC. I often have a second body (Z8) set up and with me with a shorter lens attached to deal with this, depending on circumstances.
I have not tried the Z 800, with or without TC, with faster, more erratic flyers like swallows. I’ve shot swallows with a Z9, FTZ, 500 mm PF and F 2x TCIII (1000 mm at f11). That worked well too. If I could keep the bird in the frame (a challenge at 1000 mm), the camera and lens did a good job of focusing. I’d expect the Z9 and Z 800 mm PF, with and without the Z 1.4 x TC to do better.