The exact part is the leaf sheath so I think it's bast, and in the 1970s, a German guy called Johannes Kloss started to develop its commercial use. It's a peat industry byproduct rather than a traditional material, so it's still cool but not as climate friendly as people originally thought.

Fun fact: cottonsedge fluff is generally too brittle for textile use other than as pillow or mattress stuffing, but the plant stem/root fibre, naturally retted in peat and mixed with wool, creates a luxuriously warm, light fabric. Currently unobtainium because peat is no longer considered renewable.