For code signing to work you need to trust whoever is signing the code. As you mentioned, with HTTPS, all the contents are already signed by the web server. If Jitsi published a native app and signed it, would that even help you? You still have to trust them because they could have signed anything.

Maybe you mean to compare it to a copy that has already been audited by someone else? Then you might as well use the auditor's web server to get the client (and you can do this because Jitsi can be self-hosted). So I think it just comes down to connecting to web servers run by people you trust, since HTTPS already takes care of integrity checking.