[native] make sure start_backup_handler is called only once in BackupHandler

Summary:
ENG-10001.

The asynchronous nature of this effect caused this promise to be spawned a couple of times, resulting in the starting handler multiple times.

Depends on D14095

Test Plan:
Login -> logout -> login = no issues about backup upload, user is not logged out automatically.

Added some logs to make sure there is only one call to startBackupHandler

Reviewers: bartek, tomek

Reviewed By: bartek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D14096