Refactor response handlers to improve error handling and streamline mid-stream error processing#128923

Jan-Kazlouski-elastic wants to merge 11 commits intoelastic:mainelastic/elasticsearch:mainfrom

Jan-Kazlouski-elastic:feature/streaming-error-handling-refactoringJan-Kazlouski-elastic/elasticsearch:feature/streaming-error-handling-refactoringCopy head branch name to clipboard