Very generally, to understand the role of the sein passive (Zustandspassiv), it seems helpful to differentiate between transformative and non-transformative verbs (from my experience, the sein passive is usually tought with respect to transformative verbs only, so I will focus on that case here). With transformative verbs (such as zerbrechen), the sein passive expresses the state that is the result of the - dynamic - process that is denoted in the verb. In your example, first you break the vase, then, as a result, it is broken. The speaker is focused on expressing the (at least semi-)permanent state that follows from the action denoted in the verb. This sets apart the sein passive from the werden (and bekommen) passive (Vorgangspassiv), which focus on the action.
You will readily notice that the description of the sein passive sounds less like that of a verbal use than that of an adjectival one. Indeed, many are of the view that the sein passive is actually just a copula construction. While this is controversial, the reasons why people differ on that interpretation generally have nothing to do with semantics, so to the extent that you ask about differences in meaning, irrespective of whether you treat (3) as an adjectival phenomenon or not, you would not expect any differences. That makes this a formal issue rather than one relevant for a speaker.
As far as (2) is concerned, you should keep in mind that your example is somewhat special in that zerbrechen, like English break up, can refer both to the process that causes something else to be separated into pieces, or the process of being separated into pieces (causative-inchoastic alternation). Er zerbrach die Vase. Die Vase zerbrach. That gives rise to an extra layer of ambiguity. I'm just pointing this out as I'm not sure if that was intended. If it weren't for that semantic ambiguity, it would pose no problem to tell (2) and (3) apart - the perfect always refers back to the present tense. Compare:
- [Causative:] Die Vase ist repariert. (*Die Vase repariert. Die Vase ist repariert worden.) -> sein passive
- [Inchoastic:] Die Vase ist explodiert. (Die Vase explodiert. *Die Vase ist explodiert worden.) -> perfect active
- [Causative/Inchoastic:] Die Vase ist zerbrochen. (Die Vase zerbricht. Die Vase ist zerbrochen worden.) -> ambiguous
I would leave it as an exercise to the reader to determine potential differences in meaning ... In theory, one would not expect a sein passive and a present perfect active to necessarily have the same meaning, and it is clear that, in the abstract, the present perfect active does not come with a focus on the resulting state. However, we are looking at a transformative verb and the tense indicates that the transformation has already occurred, so I don't see any meaningful remaining semantic difference. Of course, and as you are probably aware, once you start qualifying the verbal action, interpretations can become barred. E.g., oberserve that Die Vase ist mit einem lauten Knall zerbrochen bars any interpretation as a sein passive.
