[services] Backup - Create new backup - Fix checking final status logic

Summary: This simplifies the logic for checking the final status when creating a new backup in the backup service.

Test Plan: You can test this using my repo grpc-playground and intentionally launching only the backup service (without a blob service in another shell). Then, if you try to send a new backup, you'll see it works properly.

Reviewers: palys-swm

Reviewed By: palys-swm

Subscribers: ashoat, palys-swm, Adrian, atul, yayabosh

Differential Revision: https://phab.comm.dev/D4160