[lib][native][web] Use unified keyserver session recovery in lib/socket/socket.react.js

Summary:
Instead of dispatching a call from Socket, we should use the unified mechanism owned by KeyserverConnectionHandler. This way, we can avoid multiple simultaneous recoveries being dispatched at once.

It's okay to remove the SET_NEW_SESSION call here because KeyserverConnectionHandler handles dispatching this in the case where the keyserver session recovery fails.

Depends on D11214

Test Plan: Part 4.3 of this test plan: https://gist.github.com/Ashoat/75ab690d5c53cdd68a51b02e03e27c58

Reviewers: inka, tomek

Reviewed By: tomek

Differential Revision: https://phab.comm.dev/D11215