What exactly does the blockchain part of the voting app provide here? Are there any details known about how this is supposed to work, especially how to ensure that votes are actually anonymous in this case?

And using facial recognition to make sure the right person votes just sounds like it'll end up either trivially exploitable or just cause many legitimate people to be denied as their faces can't be matched.

What exactly is wrong with voting by mail? It's pretty easy to do, and it ensures anonymity by wrapping two envelopes inside each other.