`S3BlobContainer`: Revert broadened exception handler again#127405

bcully merged 2 commits intoelastic:mainelastic/elasticsearch:mainfrom

DaveCTurner:2025/04/25/S3RepositoryAnalysisRestIT-failureDaveCTurner/elasticsearch:2025/04/25/S3RepositoryAnalysisRestIT-failureCopy head branch name to clipboard