I'm shooting a Z6 with a 70-200 f/4 and 300 2.8 and regularly use the TC 14E & TC 17E.
The image quality for each lens and TC seems more than adequate. Though I have a TC20E, I just haven't had a need for the extra length...
That said, if you are shooting one of the two newer Nikkor 70-200 2.8, you'll be on the edge of adequate image quality with the TC20E, IMO. I probably wouldn't bother with the even older 80-200 since each of the several versions I've shot with in the days of film were perfect for film without adding any more glass to the combo though each suffered drastically from lots of vignetting, especially at wider apertures.
I'm now using both the 70-200 f/4 and occasionally the 70-200 f/2.8 VR II when I need a little more speed, but that's becoming rarer on my Z6 and the 2.8 I simply leave on my D800 which works quite well.
When I was shooting 6-12 MP, I had few qualms about shooting with all the Nikon TC-Es and the 70-200 VR I & II. However, as resolution goes up, adding more glass seems to lower the IQ a little too much for my tastes. YRMY.
However, perhaps with the TC20E III and the current VR III 70-200, it may be a good combo, but now with the 70-200 for the Z and the two new TCs, I'm less likely to give them a try.
Maybe the best approach is to rent a TC 20E and give it a try though I'm not certain any of the older 80-200mm lens mounts have the modified lens mounts to accept any of TCs.
