E2EE fundamentally exists for situations where we don't want to trust the server. That's the whole idea of E2EE, right?

Of course it's not black or white, security is a gradient. But if you want to check today that you are running the legit client of ProtonMail in your browser, you do not have a practical way to do it. It is theoretically feasible, I guess (?), but far from practical. But I can walk you through the steps needed to do it today with Signal, for instance.

I think I put my limit there: it's not enough to run cryptography. Verifying the client has to be practical for the user. The way ProtonMail works in the browser is a nice way for Proton to minimise the data they collect, but it's not E2EE, because even as an advanced user I cannot practically verify the client they serve me. In other words, E2EE means (to me) that there can be some kind of guarantee if you put a reasonable amount of effort into verifying it. The browser doesn't provide that at all.

Interestingly, shipping a webapp in ElectronJS (which is terrible in terms of software, IMO) is different: you can have E2EE in an ElectronJS app.

And I'm assuming that's why Signal has a Desktop app (which I believe is ElectronJS) and not a web (as in, "loads in the browser") version.