Part of [ENG-9673](https://linear.app/comm/issue/ENG-9673/implement-backupsuser-data).
Tracked in [ENG-9650](https://linear.app/comm/issue/ENG-9650/implement-integration-tests-to-new-backup-service-client-api).
I think I covered most of the cases, this is described in the code comments.
The endpoint to upload both User Keys and User Data at once is tested in `backup_integration_test`.
If anyone has any ideas about what test case can be added, I would be happy to do it.
Depends on D13878