It's really hard to come up with a sane reason why you would ever implement a PAKE with a browser HTTPS application. Probably the best-known use of any PAKE is in Magic Wormhole, where the PAKE passphrase (auto-generated) is a fundamental part of the trust model, and the application itself never touches a browser.
It's a problem with PAKEs that they're kind of neat to think about and play with, so people look for things to stick them onto. They're usually not the answer, which is why you don't see them used all that often, and why they're used almost exclusively in custom protocol settings.
(It doesn't help PAKE adoption that most custom protocols are better served by standard authenticated key exchanges based on real cryptographic secrets, rather than passphrases).
It's a problem with PAKEs that they're kind of neat to think about and play with, so people look for things to stick them onto. They're usually not the answer, which is why you don't see them used all that often, and why they're used almost exclusively in custom protocol settings.
(It doesn't help PAKE adoption that most custom protocols are better served by standard authenticated key exchanges based on real cryptographic secrets, rather than passphrases).