Sharing here what I shared in other groups:
Here is what I believe the fabric on shin is:
Close ups of her tabards seem to be VERY similar to those of Ben Kenobi in the OT which was hand woven raw silk. The weight, fraying, and overall look seem to match up. What I am not 100% sure on is her under tunic/skirt. In some pictures it seems to be a crinkle fabric while others seems to be the same fabric as her tabards. While not visible in the image provided, I believe her undersuit/flightsuit (purple color in the reference image) is made of the same or similar fabric that Sabine's is. Something to note is her pleats on the vest are not piped and rather appear to be wide zig zag stitches over frayed edges. Some areas have larger clumps of stitching.
Both Baylan's and Shin's cloaks are made out of a coating weight wool or melton fabric (or similar), this is even more apparent in the high res image. They both are lined with a lightweight cotton fabric or a stretch liner only on the hoods (EDIT: upon closer look, Shin's liner seems to have a ribbed texture). Baylan's cloak is visibly a more weighted fabric as light doesn't seem to shine through alongside it being more heavy looking/thicker. His hood has a "hem" made out of leather around the edges aside from the lining. For Shin, as mentioned by others, her cloak is much lighter and allows for light to shine through. I would have to get samples of different wool fabrics and see if any are lightweight enough to allow for light to shine through.
Hope this helps get started or steered into the right direction