I personally think that Pigeon hero with such design must probably have like, functionality of scout,high vision and map abilities together with being basically support.
Maybe instead of being named as Messenger, pigeon can be like,Oracle/being flying support mage basically and being able to see future and all around town(through connection to regular pigeons,or maybe creating/controlling spectral pigeons that we see everyone around town and using them as this character eyes)
For a gun character may have something that isn't necessary dangerous but mobile and easy to hide in robe(maybe Derringer).
Lately I will write possible abilities in my opinion.