[backup] Move authentication inside of the websocket

Summary:
Unfortunately non-native web websockets (neither in JS nor in Rust compiled to WASM) allow us to attach additional headers to the first HTTP requests that starts the websocket. Because of that we need to migrate to another approach -> client must first send an authorization message.

Depends on D11038

Test Plan: Run backup integration tests.

Reviewers: marcin, bartek, kamil

Reviewed By: bartek, kamil

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D11039