There's debate about prepositional phrases, and it depends on people's interpretation. The Cambridge dictionary of idioms, for instance, takes a wide view and happily includes them. We do too on the site, on the grounds that they might cause comprehension difficulties for learners. With phrasal verbs, some people use the term 'idiomatic', which is one way of avoiding the problem, but it can be difficult to say define things exactly:
The building's on fire.
The player's on fire. (performing well)
Here you can see a difference in meaning, with the second being an idiomatic use. Does that make 'on fire' a prepositional phrase or an idiom?
BTW, I am not sure about the categorisation you refer to.