Can't be done cost effectively
If you want it all one piece, the bottom pocket opening and stem have to be cnc milled.
It takes forever to cnc mill glass because if you take too large a bite, the whole thing xplodes.
And the stem is a very small feature, so you have to go extra slow..
It's relatively fast to cut big holes, but small shapes are difficult.
Now imagine how many passes you need to make going down 0.005mm at a time at a very slow feed rate..
If you melt glass into a mold, it won't have that perfectly uniform geometry that we're used to seeing on the plastics. You'd also still have to manually polish the damn thing.
Then, when you're done with the pocket, you need to use a Laser cnc to cut the outside features, because a cap would be too small to effectively clamp.
Small things require a bit more clamp force, try that with glass, xplode..
So lasering the external feature would be the only realistic way after the back pocketing.
The laser is really fast though, so at least that's good.
All in all, it's too work intensive, not impossible