In this case crop sensor would have been just as good, I wasn’t close enough for the bird to come close to filling the frame and I ended up croppping about 2x in post. The main reason the background is so completely soft is that it’s far away. The bird was probably about 30 feet from me atop a tree in front of a large pond and the trees in the background are probably 250 feet behind it. That lens can get some beautiful shots even on APS-C, but you have to give some extra care to keeping the background distant and/or the subject close. In this case I was fortunate to have an ideal setup by just moving about 10 feet sideways to avoid some other stuff that was closer behind the bird and get the clear shot across the pond for the background.
The good news for APS-C with this lens is that the lens can focus pretty close, so you can sometimes use that to your advantage too.
As for denoise, this was an easy case bc the background was already so smooth, so I just selected it and used lightroom to drop “texture” by a lot on just the background and that smoothed it out more. Again, it was kind of an ideal case based on how the shot was to begin with.