[backup-client] set backupID after uploading User Keys

Summary:
Part of ENG-9656

We're going to store this in Redux too, but it's needed for native backup logic and was previously implemented for uploading User Data compaction, adding this for User Keys too.

Depends on D14000

Test Plan: Tested creating backup and secondary device login

Reviewers: bartek, tomek

Reviewed By: bartek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D14001