"We were broken up" could mean that external forces split them up as a couple, for example, their parents.
"We were broken up" also means "we were devastated" - eg. by the death of one of their friends - and nothing to do with the couple parting ways.
The reason you can't learn all possible expressions in a course, or from a book, etc. is that there are too many, and yes, there are also different ways of saying the same thing.
Student or Learner