Depending on how it's batched, this tells HIBP (and any MITM -- even one that can only see ciphertext) roughly how many unique passwords you use. Knowing the 5-character hash prefix also cuts down brute force attacks by a factor of a million -- though in practice this is only a real issue if you use one of the compromised passwords (there's only a few hundred candidates per prefix), in which case you're kind of screwed already because they're probably in dictionaries anyway.
I don't think these are /critical/ issues and the latter is basically just an argument against the HIBP service, but the point is that a user should opt-in to sharing their data in cases like this so they have a chance to make an informed decision. The k-anonymity design of the HIBP service has a degree of anonymity, it's not "provably anonymous" like homomorphic encryption or similar schemes would be.
I don't think these are /critical/ issues and the latter is basically just an argument against the HIBP service, but the point is that a user should opt-in to sharing their data in cases like this so they have a chance to make an informed decision. The k-anonymity design of the HIBP service has a degree of anonymity, it's not "provably anonymous" like homomorphic encryption or similar schemes would be.