In your original comment, it seemed like you were suggesting hashing only before transmission

Ok, that wasn’t what I was suggesting, no. That would effectively make your password hash the password itself

how does such a service (like Proton Mail) perform this in a web browser without having access to the data necessary to decrypt all of the data it’s sending?

Yes, pretty much. I can’t really find a good, detailed explanation from Proton how it exactly works, but LastPass uses the same zero-knowledge encryption approach - which they explained with some diagram here - with a good overview of the client/server separation of it’s hashing.