Unfortunately, as per your question, unlike many of the knowledgable members here of uHH, I am not intimately familiar with every piece of equipment that I do not use or have first-hand experience with. Some of us professionals are kinda boring as compared to camera collectors or the folks that are continuously changing up their gear. If, however, you find your preset gear is not addressing your needs, it is best to arrange an in-person demonstration of the various makes and models you are considering.

In my own cases, I find a make and system that addressed my requirements and use it until it no longer addresses my needs or finally disintegrates. Usually, when I am finished with a camera it has little or no resale value!

My advice is to stick with compatibility. Select a camera that is compatible with your present lens inventory, unless you want to reinvest more glass. For a number of reasons, I started with Canon gear when I finally transitioned all my studio operations to digital. Nothing wrong with Nikon or Sony, it was just that I had some special purpose Canan glass from my previous film systems.

For me, it is difficult to advise on a camera or system for anyone else. It's a matter of ergonomics. Each person has different levels of dexterity, the ability to steady large cameras and lenses, and of course specific photographic needs.

As for cross-brand adaptation, just make certain conversion will accommodate prop focusing at infinity, etc.

At the time, I have no need for a mirrorless camera. Perhaps they are more nimble and handy for fast shootg situations. After many years of shooting action, sports, events and more with big bulkey large and medium form film equipment and heavy flash units, my preset DSLR system seems almost weightless.

As for flash, again the compatibility things are important. I do most of my flash work in manual mode but if you depend on TTL exposure management, you need to make certain that your flash gear is compatible with any new camer system.

Please see my other post on my lenses. I sure do like those Sigma's. Going down on file size is out of the question. I agree with you. Why the change? To save some weight and size, to improve sensor quality, in-body stabilization, and better focusing. I am not sure how noticeable the difference in sensor quality might be, the stabilization is not that big of a deal for me. The focusing is. For still or nearly subjects, the 80D is fine. For sports and wildlife in motion, I am never quite satisfied with the 80D focusing performance. I do not know how much is myself or the camera.

I think IBIS is a game-changing mirrorless technology. But, it needs to complement other positive developments. It's not worth it alone.

In general the size benefit is negligible, but does depend on the specific cameras and lenses being compared. As long as full-frame lenses remain involved, the weight difference many times makes no appreciable change, even if the size is reduced.

Your EOS 80D might not be as sophisticated as a few options on higher EOS tiers. Your EOS 80D has many of the same advanced options in AI Servo as these higher-tier cameras. Adapted lenses onto the Sony body are extremely unlikely to perform as good as natives lenses on their native bodies, especially for action. The EOS R had a firmware update for eye-tracking AF, but I wouldn't expect the EOS R to perform noticeably better in a compelling way to change.

Focusing for sports / wildlife includes both the camera set-up and shooting technique. If you have done so already, the best approach is to post unedited JPEGs demonstrating issues with a focused discussion on actionable ideas specific to those images, and the camera and lens settings.

For the other questions about adapters, the EOS mirrorless camera are a native RF mount. Only Canon RF lenses will mount directly to these bodies. The EF-RF adapter supports all Canon EF and EF-S lenses. Third-party EF lenses should work fine with this adapter too, but Canon doesn't make any claims about non Canon equipment.

I am mulling over going from my Canon 80D to either the Canon EOS R or Sony A6600. I have several Sigma lenses and a Canon flash. Either camera would require a lens adapter and the Sony would require a new flash. The Canon is in stock while the Sony is backordered. The Canon is full-frame while the Sony is APS-C. Neither this nor the file size is a significant matter to me. I do like the smaller Sony body. The main thing I am looking for is great accuracy in focusing. People, sports, wildlife and flowers are my main subjects.

What would you advise to do: stick with the 80D or switch to the R or A6600? Or do you suggest another move?

Thanks in advance. Please stay on topic.