You are absolutely correct, with some caveats. Browser client can generate keys on clientside and allow to offload them as a file to be used on other devices. Our own web XMPP client does that. But Protonmail does not work like this.

Verification is very simple: if you log in on a new device and see all your content while using only login and password to authenticate yourself, then the content stored on a server is NOT encrypted and is readable by server owner.