Looks like this doesn't include another feature of HaveIBeenPwned. Its cracked password hash database. If you trust their JavaScript, you can type in your passwords and see if they are on the list. If you're a little more paranoid you can download the hashes and do your own search.
Since this service appears to be deliberately aimed at non-tech-savvy users, I get the impression that Mozilla is trying to not normalize the practice of submitting your passwords to third-party websites. It also nimbly sidesteps any questions of "why should I trust firefox.com with my password"; you don't need to, because you're not giving it to them.
Well with the API it’s pretty easy to test your password. You just have to hash it, send the 5 first characters and it returns the list of the hashes starting with those 5 characters.