AF-S 50/1.8G uses the rack focus method, and thus its focal length is firmly fixed. I surely observe the breathing when I tried focus at a subject.
Perhaps the optical system should work to cancel the change of the magnification factor when focusing by changing its focal length.
The problem is that people are using "breathing" to mean two different things. The first is cinematic definition, which is that objects change apparent size as they move in and out of focus. That's what you see with your 50mm f/1.8G and virtually every other lens designed for still cameras. Zeiss Master Primes and a few other cine lenses use "dual floating elements technology" to greatly reduce this type of breathing and were marketed as "Breathless." But as a result, unlike the 50mm f/1.8G, they do change focal length with focus distance.
The second use of the term is to describe lenses which change focal length with focus distance. If a lens has floating elements, be they to provide rear focusing, internal focusing, CRC, or for other reasons, it's extremely likely that it exhibits this type of "breathing" to some extent. Lenses like the 70-180mm Zoom-Micro-Nikkor, the 70-200mm f/2.8 VR-II, and the 28-300mm's do this to a greater extent than people were used to. I can't speak to the 28-300mm's, but in the case of both the 70-180mm and 70-200mm it was a deliberate design decision. For the 70-180mm, the designers wished to cancel out the "bellows effect" and keep an effective aperture of f/5.6 through the focus range. For the 70-200mm VR-II, the designers used the compensator group to focus the lens, which limited the amount of glass they needed to "push around," resulting in faster focus speeds.
My back of the envelope calculations show that at minimum focus and maximum zoom, the new lens has an effective focal length of about 191mm. So the second type of "breathing" will be less of a factor. My guess is that we won't know how much "breathing" it has by the cine definition until the inevitable unboxing videos.
