The composite structure within a schedule uses the attribute number to define the list order and not the actual text included within the composite name. The screenshot below of my schedule has the Composite Structure set to descending, which can be seen to be working when shown alongside to the screenshot of the Attributes Manager.
I haven't worked out why this is the case but it explains why the ascending/descending option does little to help with alphabetical text organisation. Unfortunately I'm also unaware of any sort of workaround.
ArchiCAD Versions 17-26 2019 MacBook Pro - Intel Core i9 @ 2.3GHz, 32GB RAM, AMD Radeon Pro 5500M, macOS 12.6