[tialaramex]

No, I doubt it would be considered for browsers in the immediate future. OPAQUE was chosen by CFRG as the asymmetric PAKE that IETF protocols should choose by default in future. If you're designing a new protocol and it needs (or should usefully have) an asymmetric PAKE, then the IETF would prefer OPAQUE.

For a web browser, as I wrote, the correct thing is to push hard for WebAuthn.

You are correct that as a user, today, you are obliged to have some sort of password store if you want reasonable security, but that's a constraint imposed by the past, rather than a way forward.