You don't submit to the API either a full password or a full hash (which, since Troy produced the hashes is identical). A hash is pretty much perfect for K-anonymity because if you use a prefix like this then it's extremely likely your data will be spread across the buckets, so no 5-character prefix is close to uniquely identifying a password.
As stated in the post, it's a simple solution to help with anonymity.
"The password has been hashed client side and just the first 5 characters passed to the API As mentioned earlier, there are 475 hashes beginning with "21BD1", but only 1 which matches the remainder of the hash for "P@ssw0rd" and that record indicates that the password has previously been seen 47,205 times."
But's it's not always that hash. The password you're checking may not be on the list. This is just a quick check to see if the password in question is on the list, in which case it may be a poor choice depending on how often it's seen.
For example, say I want to check "gSAey27tgGsaEG". That hashes to c2e5dfb023cd42df94751581cba33b24bc011027. https://api.pwnedpasswords.com/range/c2e5d has no entry for fb023cd42df94751581cba33b24bc011027, so it's not even in the list of passwords.
Put another way, it averages a few hundred hashes per prefix based on the total password list size (~500M), but there's 2^136 possible has suffixes per prefix. There's no point in guessing that.
Forgive my ignorance but why is submitting a hash a problem? Because Troy knows which passwords have been checked? Why should I care about that? I get that it’s like submitting your password in the clear if it’s in the DB, but in that case surely you have bigger problems.
One way that sites can use this service is to check whether a password has been leaked when users sign up. By handing over the SHA-1 hash of the password you're effectively trusting this service (and anyone who might have compromised it) with all your user's clear text passwords. Connecting the right password with the right user can be trivial in some circumstances, say because a site has a publicly visible sign-up date on profiles, or even if it just hands out sequential IDs to users.
