[native] Have BackgroundIdentityLoginHandler wait until LogInHandler

Summary:
This addresses a race condition described in ENG-8785, first investigated in ENG-8772.

Depends on D12697

Test Plan: I reproduced the issue by following these instructions, but making sure to log in with SIWE. Before this diff the issue reproduces; after the diff, it no longer reproduced

Reviewers: tomek, inka, varun

Reviewed By: tomek

Differential Revision: https://phab.comm.dev/D12698