A few thoughts:
The Z7II isn't out, so we don't know for sure. But I won't let that stop me! I use both DSLRs (D500 and D850) and mirrorless (Z6 and Z7). I am planning to upgrade my Zs to the Z6II and Z7II.
For landscape use, unless you care about two card slots, I would expect the Z7 and Z7II to be essentially equivalent. Autofocus for landscape use should be better with either of those models than your D810 (which of course isn't bad at all -- I had one before I got a D850). I think this is (i) because focus points cover the frame, so you can focus wherever you want; (ii) focusing on the sensor seems more precise and repeatable; and (iii) there is less need to focus tune lenses. If you go with some native Z mount lenses, you will also find that they are often better than their F mount counterparts, especially in the corners and at the edges which can be nice for landscape use. (No criticism of DSLRs and F mount lenses -- I have liked mine for a long time and still use them.)
For wildlife use, I would expect that the Z7II will be better than the Z7. Steve and others have noticed improvements in the autofocus system in the Z6II as compared to the Z6. I would expect a similar improvement in the Z7II as compared to the Z7, although we will want to see when the Z7II is in people's hands, especially Steve, Thom Hogan and Brad Hill. The Z7II also has a bigger buffer, which may be useful for BIF and other action. I believe that Steve said on this forum that while the Z6II is not up to the standards of a D6 or even D850, it "gets the job done" for BIF.
The Z7 and Z6 are already decent wildlife cameras and I expect the II versions will be better. Not all birds are in flight. I often photograph waterbirds, wading birds, and perched birds -- in these cases, I prefer my Z7 with a 500 mm PF over my D500 or D850. I have also shot BIF with the Z7 and 500 mm PF (sometimes with a 1.4x TCIII). It's not bad, once you get to know and get used to the autofocus system, especially for larger and slower birds - eagles, swans, sandhill cranes, egrets, geese, pelicans and the like. The autofocus system is different than the one in Nikon DSLRs. Steve's book on Nikon mirrorless autofocus would be very helpful (I believe Steve has said he is planning to update it for the new ZII models). Also consider Thom Hogan's e-books on the Zs (there will be a new one for the Z7II and Z6II).
Many compare the Z cameras to the D850. But you have a D810. I recall the D850 was a material step up from the D810 as a wildlife camera. You may find that the Z7II is also a step up from the D810, even if it is not quite a D850.
There are some things in the Zs that Nikon could and should improve with firmware -- e.g., allowing selection of autofocus area with a single button press. I am hoping for firmware updates to the Zs, especially the ZIIs as we go forward. No guarantees here, although I would think it would be a smart move for Nikon. One thing that may or may not be fixable with firmware is the slideshow effect when using high extended to get more FPS. It makes following BIF difficult, when compared to the slower, regular high mode or to a DSLR.
All that said, there's nothing wrong with a Z7 and D500 combination. I used that combo last year on a trip to Gwaii Haanas (the D500 with a 500 mm PF and the Z7 with a 70-200 mm f2.8E FL lens). As things stand now, purely for BIF and other fast action, the D500 (and D850) is better than the Z7 and Z6 and probably also the Z7II and Z6II.
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