So since you have seen the same fakes and sure about it.
I respect your eye.

but my own tricks to identify agate or carnelian are
the aging signs on the surface and the polishing signs ...

you can see the shinings (from the surface of the carving side and other sides ) are consistent and that means the same aging extent.

So if the bead is old(I am sure about it) ,I do not think the carving side is newly cut...

as to the carving (cuts) itself... I think you are right but what I want to say is In china wheel-cut had been adopted pretty early ...how could not this kind of tools used by others of the same age?

forgive me for my poor english

R.M.