[services] Rust Integration - Backup - Make check_error shared

Summary:
Depends on D5030

I just moved the function check_error to the mutual space tools following the DRY rule.

Test Plan:

cd services
yarn run-integration-tests backup

Works as before

Reviewers: jon, max, varun, tomek

Reviewed By: tomek

Subscribers: ashoat, tomek, atul, abosh

Differential Revision: https://phab.comm.dev/D5031