[services] Backup - Blob Get Client - Cleanup

Summary:
Depends on D5096

Linear task: https://linear.app/comm/issue/ENG-1734/improve-error-handling-system-in-the-blob-client

Removing ERROR_MESSAGES in both client.

For the put client, deferring handling an error to only one place in the code.

Test Plan:

cd services/backup/blob_client
cargo check

after running localstack, blob, and backup (in this particular order), this still works:

yarn run-integration-tests backup
yarn run-performance-tests backup

Reviewers: jon, max, varun, tomek

Reviewed By: jon, tomek

Subscribers: ashoat, tomek, atul, abosh

Differential Revision: https://phab.comm.dev/D5097