It doesn't matter that it theoretically all happen in the browser. You can serve different versions to different IPs etc. Every heuristic in me would be screaming don't use that if I would have a need for such tool.
See also https://haveibeenpwned.com/Passwords.
HIBP offers you a way to validate a password has been compromised, HIBP does not offer you a way to determine it has not been compromised or is otherwise suitable for use. It’s a service for excluding compromised passwords from use.