I've shot for the past few years with a D500 and Sigma 150-600mm C.
This year I put about 5000 frames on a D7200 for fun and giggles and got the chance to try out an R7 and 100-400mm II with the 1.4x TC.
Here's my take on it all:
1) Just getting a used D500 and using it with your Sigma 150-600mm C will get you better results as that pesky f6.3 at the tele end really holds back the D7200 AF system.
2) The R7 is an impressive camera and decent bang for buck. The AF, even with the 1.4x TC was quick to acquire the subject and it was quite sticky.
3) There are situations where a D500's AF will be superior (e.g: Dragonflies in flight or birds with branches and leaves in front of them).
4) The 100-400mm II is surprisingly sharp and it takes the 1.4x TC quite well.
5) The R7 EVF is quite poor and the rolling shutter and small buffer really makes it a 15fps camera not a 30fps camera. Also, the build quality feels more consumer level than the solid chunk that the D500 feels like and adding an adapter to the mix really made me feel uneasy.
All that being said, which one you choose depends on what your plans for the future are.
If you plan on upgrading your gear again in the next ~3 years, then I wouldn't recommend either the D500+500mm PF or the R7 and 100-400mm II.
If I were you, I'd be looking at either Z6 III (as it inherits most of the Z8 AF) and a Nikon 180-600mm or at a Sony A6700 and either a Sony 200-600mm or Sigma 500mm f5.6 as both systems have a more logical lens layout for wildlife shooters, plus a decent body upgrade path.
If you don't plan on upgrading your gear again in the next ~3 years and you want to keep it 5+ years, then again I wouldn't recommend either the D500+500mm PF or the R7 and 100-400mm II.
I'd get an OMDS OM-1 (ideally the mk. II version) and the Olympus 300mm f4 and 1.4x TC.
I actually did get this kit one year ago as an upgrade from my D500 and 150-600mm and after using the R7 and a few other systems this year, I'm happier than ever with my choice. I don't actually think there is a better bang for buck wildlife set-up (but I do plan on shooting it into the ground
).