Pax in commercial transport is used as something like persons or passengers, in the context of counting people, e.g. 150 pax onboard.
I observed that in German writers tend to use the meaning:
PAX = Persons approximately.
(Source: European Union and the Committee of the Regions)
Pax isn't exactly shorthand for Passengers. It's short for Passengers and Passes.
Cargo is known as "cargo", but passengers are called "pax" by the traffic department, who puts them on and takes them off the airplane and "bodies" by the crews who fly them.
Pax could be from passenger as usually assumed in the Aviation community, albeit I don't see why not *pass" instead. I wouldn't be surprised it comes from the merchant navy.
Can we track the use further back to the origin in aviation field?