A few reflexive verbs are tucked away in some of the exercises in Italian (and Spanish), but there don't appear to be any exercises devoted to this topic like you'd find in a course book. Duolingo takes a rather non-traditional approach and doesn't seem to provide much depth in reflexive verbs apart from the use of il "si" spersonalizzazione construction, e.g., "In Italia si mangia bene" which pops up more often.

That's unfortunate. Reflexive/reciprocal can be tricky when combined with object pronouns, especially in the passato prossimo. They deserve a special category for practice.