The assassin upgrade is earned through stealth kills. I have successfully done loads (cloak + press V when prompted) but they are not registered in the upgrade screen (H).

Is this a known bug?

I assume it's equipped.. So no, sorry. Hope you solve it, can't help atm

I have certainly used an upgrade pack on the module but not sure it's equipped because I've scored 0/20 stealth kills. Other modules are registering their progress towards their respective goals but not this one.

I wish I could help, but my rig is a 1000km away so I can't test it, but I'd try with it equipped if not