transparency in 3D models created in Blender

Procedural (generated) materials cannot be transferred between any software, at all, for the most part. If you use USD filetypes, the softwares have a way to tell each other what to do, but whether the other software has the ability to try to do that thing, or is designed to do it when told is another issue entirely.

The issue you have, though, is probably that AE doesn't support that material. I.E. it doesn't know what to do when handed a translucent material. Glass materials are handled through effect tricks last i tried, though you'll want to try using a transparent shader, a glass shader, using a PNG material with alpha, etc. Just to make sure. This is the art of making passes. With an alpha pass and a normal pass you should have what you need to approximate glass without properly rendering it.

Also, for the procedural stuff, you'll need to bake those materials into textures. It's not totally necessary, but also check out n-gons, becayse those can mess with materials too sometimes. try setting the materials to 500 or 300 scale. Even a 16k texture map might not be enough for such fine detail, and a normal map might be more dynamic.