Other silent gear items can have affixes added to them with no problem, but this axe won't go into the table. Silent gear added ATM support with the move from 1.20 to 1.21 so it may be something being worked on, but it's a thing that currently doesn't work. I havent tested it with other ATM items, so I also don't know if this is just a fluke.

Weapons are picked up as weapons by presence of the default Attack Damage attribute modifier on the item; if the silent gear axe doesn't have this modifier, for whatever reason, it will not be picked up as a weapon.

If it is an issue unique to SGear's ATM heads, I expect they forgot to set something up for thos heads.