Answer to almost all of your questions is that it entirely depends on the service what kind of auth implementation they offer. I personally have completely adopted passkeys and use them with every service that allows it.
I use ProtonPass and have made it the default password store on every device and browser. This way all passkeys get stored in proton and I can login from any other personal device with proton setup.
> ...it entirely depends on the service what kind of auth implementation they offer.
I think that's exactly the problem. These are all answerable questions, but getting those answers is confusing for most people.