Is it possible to have a web browser delta chat client?

User is able to scan qr code to login, and can self-hosted the client on their own server.

not yet, probably in the future it will be possible.

Though you might not want it because you loose E2E encryption if you host on some random VPS server.

Another idea was to run the “server” on their android phone (iOS does not allow the app to stay active In background, so there it would be impossible) and connect via local network.