Question- is the cost of increased manufacturing time offset by the benefit? If so what benefit does this give that a normal stone, or one ground with a slight point but no groove does not?

Haven't tried this projectile yet, but I can see how it would would roll out of the pouch differently and perhaps cause less friction than the biconical shape (meaning cleaner releases).
Biconicals are not ideal for a flat pouch because the projectile has to do a balancing act, and lateral motion will put the projectile out of perfect alignment. The grooved projectile would be much more stable under the same circumstances.

I noticed that it has a diabolo shape, like an airgun pellet.  With a rifle spin, it would be pretty stable.

You can shoot it like a biconical gland too.  It can open with the tip or across.  It depends on how you shoot.  The interpretation is difficult.  That's why I try to bring some order.  Mesh countersinks only make sense if there was water nearby.  But even then, this use is questionable.  Mesh countersink are lost.  Like ammunition too.  The argument that it would be too laborious therefore applies to both.  Clubs.  In fact, that's a good explanation.  When they are made of stone.  A club made of clay or very small stones makes little sense.  So I'm not saying that these stones were all hurled.  My aim is to differentiate.  And what Hubert says is not true.  The hollow is not a disadvantage.  But on the contrary.  If you have a woven letter, the fabric will adapt to this hollow groove.  The sling will open very quickly.  Try it yourself. The Cordaillot Sling is very small.  Yes, filigree.  In addition, it is very complex to manufacture.  Unusually expensive for a sling.  I came across this shape because it almost comes naturally.  I fired thousands of these projectiles with it.  It works great.  I think I have enough experience to come up with such a theory

To me this design just screams out to have cordage wrapped around it.  Whether that's for a bola, sinker, or any other kind of counter-weight.

I do have a thought on this being used as a sling projectile though.  Something the groove reminds me of is the fuller on a sword.  A sword fuller is intended to reduce the overall weight of the blade.  Could this be used for the same purpose with a sling projectile?  If a very dense material such as lead is being used, having the groove around the center would reduce the overall mass.  Which means you could have a projectile with the same effective length and diameter of a biconical shape, but with less overall weight.