Just making sure I am reading this right:
The rules on critical specialization say that they apply when you "make an attack" and "get a critical success"; they don't specify what kind of attack it has to be.
Am I correct in reading that since the Trip action has the attack trait, this would mean that for example if you are using a fauchard to trip someone and get a critical success, you could move them 5 feet in addition to tripping them?
That looks correct to me. I can't find any language restricting the attack roll to specific types of attack such as Strikes.
It would appear to be the case, yeah.