When the word "volume" is used in sport science research, it is referring to the number of total hard working sets per week (a hard working set is a set taken with 5 reps from failure). Yes this means that "high volume" means a lot of working sets, not a lot of reps.

In order to track and progress volume, it would be good to see the number of sets sets programmed on a per muscle group basis. At the moment, the only way to do this is to manually count sets.