Hahnemuhle already offers its own baryta paper, Hahnemuhle Photo Rag Baryta, which is much more durable and has a better 'feel' than IGFS, while having similar print qualities. It also has a non-baryta version, Photo Rag Pearl, which prints very similarly, while being even more durable. What does Photo Silk Baryta offer that the other two don't? Is it smoother, better Dmax, glossier, etc.?
Why Hahnemuhle has put this paper on the market, while, whereas you mention only one, they already have 3 baryta's (outside of the Harman baryta's), is something the Hahnemuhle suits can only explain.
They position HPSB as an alternative to IGFS, and whilsth the paperbase (incl baryta layer?) appears to be the same, the ink receptor coating definitely is not the same. The numbers part of my test shows this, and when profiled it gives more gamut (~10% according to the ColorCheck method), very smooth tone from white to black. The Dmax is 2.3 compared to ~2.4 on IGFS, so slightly less, but can be fine-tuned to a higher value if must be. But those are numbers, and show only half of the story.
From a image experience perspective, skin tones, hair tones, transitions from highlite to shadow to my eye are better, above all this experience of realness, as the persons portrayed are sot of "there", intead of watching a print, which is very good. And this while its surface is not glossy.
Of the ones you mentioned, the Photo Rag Baryta i played with some years ago and preferred the Harman Gloss Baryta as better. The Photo Rag Pearl i have no experience with, so i cannot comment on that one.
But of all the non gloss papers, so the satin or luster surfaces, i have been able to print on, the photo silk baryta has the most 3-dimensionality, realness, or however you can call it in english. Yet with reduced specular reflections, not bad at all.