This is a classic failure to see the forest for the trees, and it's something I try very hard to train out of young scientists.
To answer your questions:
1) Yes, f/5.6 allows you to shoot at lower ISO than f/7.1.
2) Yes, f/5.6 gives you a shallower DOF than f/7.1.
How about these questions?
3) Does a 26 MP sensor deliver more resolution than a 24 MP sensor?
4) Will a shutter speed of 1/10000 s freeze motion better than a shutter speed of 1/8000 s?
Obviously the answer to both of those questions is also yes. But the relevant question is do any of the above affect photographic output in a meaningful way? The answer to that question is possibly but only in relatively rare, very specific circumstances.
At any ISO of less than 12800 with a modern FF sensor, 2/3 of a stop of ISO is not going to make a significant difference in the result after good NR. ISO 640 will not be visibly different than ISO 400, both will be essentially noise free. Even ISO 40000 and ISO 25600 will not be meaningfully different, both will be either noisy or lose a similar amount of detail from NR. Now, perhaps ISO 51200 will give you a barely usable shot after NR that ISO 80000 will not. How often do you shoot at those ISO values where you must use the resulting images?
With a 500mm lens at 10 m, f/7.1 gives a DoF of 16 cm and f/5.6 gives a DoF of 13 cm. Say you're shooting a mockingbird, either way the entire head will be in focus and the tip of the tail will be out of the plane of sharp focus (within the assumptions of a DoF calculator). As the examples show, the background separation is not meaningfully different. You say you sell pictures for supplemental income, has any editor/buyer/etc. told you, "Sorry, it's a nice picture and it's
almost good enough...I'd buy it if only it had a very tiny bit more background blur?" Somehow I doubt it. As you say, you're your harshest critic and you've convinced yourself that 2/3-stop will make your pictures better. And even so, as
@AlanF demonstrated, post-processing can make a much bigger difference anyway.
To finish off the other points, there may occasionally be some small, high frequency feature within an image that can be resolved by a 26 MP sensor but not by a 24 MP sensor...assuming resolution of that feature is critically important, there are far easier ways of making sure that feature is resolved than counting on a 2 MP difference (with the correspondingly much smaller linear resolution difference). Similarly, for the vast majority of subjects 1/8000 s is more than sufficient to freeze motion if desired, and for those subjects where it's insufficient, 1/10000 s will be likewise.
That was in reference to your desire for a $3-4K 500/5.6 lens. Canon will sell somewhere over a million EOS R system cameras this year. Lenses costing $3-4K are going to sell in thousands of units, i.e. a very small fraction of the number of EOS R cameras Canon sells. It's the same failure to see the forest for the trees, thinking that if Canon releases a lens that induces a few thousand people to switch to the EOS R system, that is a 'bigger market segment' relative to the million R bodies already sold per year. As I pointed out before, it's the unique offerings of lenses like the
600/11 and 800/11 that are likely to entice a meaningful number of buyers into the R system.
Now here's an interesting point... You've stated that you have the RF 100-500, and throughout this discussion, you keep mentioning that a 500/5.6 is your dream lens, that f/5.6
would provide (conditional tense) better background separation but not cost as much as the f/4 supertele lenses. Maybe I'm reading more into this than what's there, but your statements suggest that you don't actually have a lens capable of shooting at 500mm f/5.6. If that's the case, it certainly explains why you won't post any examples demonstrating how 500/5.6 is better than 500/7.1. But it also means you're making conclusions based on zero actual experience, and discounting both the experience of people with such lenses and empirical testing that shows results contrary to your unfounded expectations.
Finally, as you said previously you are the one who gets to choose both what you want and what you buy. Since your 'dream lens' is a 500/5.6 costing $3-4K, and Nikon makes just such a lens, why dream? By all accounts the Z8 is a very capable camera. Sell your RF 100-500 and whatever body it's attached to, and that should cover most of the cost of the Z8. Buy the Nikon 500/5.6 PF. If you need to make up the difference in the Z8 cost, there are Used Like New copies for $2100. Buy the Nikon Z8 and the lens with your ideal specification and live your dream!