I think your sphere is happy that we are talking and enjoying it, regardless of whether we come up with an accepted label.
Since you are attracted to agate and this sphere feels different, I'd trust your feeling. The circular marks and lines of white mineral remind me of orbicular jasper I have seen. I have two orbicular jasper spheres (ocean jasper, but that's trademarked so we have to call it orbicular jasper now), but they are heavily orbicular. I'm still unable to post photos or I'd show you.
Stones don't always carry characteristics throughout, sometimes having only a hint of a clue. Experienced geologists often can't agree on the identity of a given stone, so I suppose we are doing okay.
The other stone your sphere looks like is the emerald in matrix. I have a much smaller emerald with quartz sphere that has many similarities. The differences are no circular markings and a lot of sparkles when the light shines on it. Maybe pyrite or mica?