[services] Backup - use anyhow::Result short form

Summary:
According to the Rust docs:

Use Result<T, anyhow::Error>, or equivalently anyhow::Result<T>, as the return type of any fallible function.

I replaced all occurrences of anyhow::Result<T, anyhow::Error> with anyhow::Result<T>.

Related Linear issue: ENG-1841

Test Plan:

• Backup service container builds.
• Integration tests pass.

Reviewers: jon, marcin, tomek

Reviewed By: jon, marcin, tomek

Subscribers: ashoat, atul, abosh

Differential Revision: https://phab.comm.dev/D5299