[backup] Use authenticated service trait

Summary:
Implemented the trait introduced in D12507 for BlobServiceClient and used it in backup handlers.
This simplifies the code and makes it more flexible and future-proof.

Depends on D12507

Test Plan: Tested backup service locally - blob requests are successful for both authenticated and unauthenticated HTTP endpoints

Reviewers: kamil, varun, will

Reviewed By: kamil

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D12508