I use a 500 f4 G for about 9 years now and it's sad to hear - sorry - read, that you have this kind of problem, because it's a great lens as long as nothing is broken. So here are my 2 - maybe 5 - cents.
Admittedly I haven't read all posts but only your initial one and a few others.
1. Filter
I can confirm that the standard filter must be in the lens to get proper results. I can't tell you why, but this was a general issue with some of the G series long glass. At Photographylife I remember to have read something about a test the have done with a AF-S 200-400 F4 G VR, which clearly showed a significant drop in IQ when testing the lens with the filter removed.
Thus, it's a good idea to fix that first If you have the holder a high quality 52mm NC filter is all you neet.
2. Camera
I hope I didn't overlook something, but in the initial post I couldn't find what camera you are using.
If you use a DSLR the reason can be a missing AF fine adjustment for the lens. In DSLR time any glass with 300mm or more went though this procedure. It is a standard function provided by the DSLRs and all you need is a bit of time, a second tripod and something called Spyder LensCal (or similar devices).
If you use a Z camera with FTZ this is not an issue. I use the 500 f4 G on a Z8 and it renders nothing but excellent results with the only reason not getting tack sharp images is myself
. If the lens shows the bevaviour you describe on a Z body it is very likely that something is wrong with the lens. The F-mount 500 f4 - even the G generation - still belongs to the sharpest super tele lenses Nikon has made to date.
3. The lens itself
Providing that the lens is o.k. mechanically, i.e. it hasn't been dropped so that the flange or some glass is out of position, there are two things that could cause this kind of problem:
- Defective AF motor
Happens very rarely but it happens. The last repair I can recall from somebody happened to be on a 500 f4 G and costed about 250 € here at Nikon Germany.
- De-adjusted VR unit
Sounds weird when having an issue that you would relate to AF, but it's true.
It can happen either by mechanical impact to the lens, that would not cause mechanical damage, but enough do deadjust the VR unit , particularly while VR is working or - this information I got directly from Nikon recently - by not following the correct procedure when switching off the VR on Z cameras. Nikon explicitely recommends to switch the lens VR off ot the lens before swithcing the camera off.
If you switch the camera off while the lens VR is working this can lead this kind of adjustment sooner or later.
Good news ist, that this is something that noemally doesn't require spare parts, but can be solved with an adjustment that they would do as part of a normal lens inspection.
As mentioned befoe, step one should be the filter.
If you then take the advice given above to look at some test photos with Nikon NX Studio, you will be able to see which AF sensor was actually used for each shot and that's where the image should be tack sharp - and I mean REALLY tack sharp -, because we are talking about a lens with proven Imatest figures of well beyond 3000 for resolution, which is around 45% more than your 200-500 at 500mm.
In fact you should see much better results with a 500 f4 G being in proper shape compared to what you are used to see from you 200-500.
If you can see there that the sharpness peak is not where the Nikon software shows the active AF sensor for the shot, but somewhere else in the image, it's time for AF fine adjustment.
As recommended above the test images should be shot with good light, stable support and VR switched OFF. In fact the G lens VR didn't seem to like sitting on a tripod for some reason and even if the switch says "Tripod", just switch it off.
If with all that taken into account you don't just get images with the sharpness in the wrong place but entirely soft images, I think it's time for a Rendez-vous with Nikon service. In the end it will save you a lot of time and nerves.
You are right with loving this lens, I can tell you. And I - well, I think most of us here - wish you all the best to get that sorted.