With /passkeys/, actually! It's more generic than just hardware keys. I don't know of any good implementation yet, but there were a few projects on github mentioned in some passkey-related discussions here.
I do not use anything like iCloud or Windows Hello and I don't know what these services actually use, but if they implement these open standards, it's only a matter of adding some glue code. I'd say it's likely that Putty will implement this over on Windows eventually. That is my speculation, as I said, I don't actually use any of this.