### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

When a transcription job is scheduled I specify `OutputBucketName` and `OutputKey` to store the transcription, when the transcription job is complete, I check if output transcription is put there. Unfortunately, it's not there.

### Expected Behavior

Output transcription should be stored on S3 at the given bucket and key.

### How are you starting LocalStack?

Custom (please describe below)

### Steps To Reproduce

Using Test Containers 

Reproduced in project:  https://github.com/kkocel/local-stack-transcribe-repro


### Environment

```markdown
- OS: macOS
- LocalStack: latest
```


### Anything else?

_No response_
}
                        ],
                    }
                )
            output = {
                "jobName": job_name,
                "status": TranscriptionJobStatus.COMPLETED,
                "results": {
                    "transcripts": [
                        {
                            "transcript": tc_result["text"],
                        }
                    ],
                    "items": items,
                },
            }
            
            output_s3_path = job["Transcript"]["TranscriptFileUri"]
            output_bucket, output_key = get_bucket_and_key_from_s3_uri(output_s3_path)
            s3_client.put_object(Bucket=output_bucket, Key=output_key, Body=json.dumps(output))
            
            job["CompletionTime"] = datetime.datetime.utcnow()
            job["TranscriptionJobStatus"] = TranscriptionJobStatus.COMPLETED
            job["MediaFormat"] = MediaFormat.wav
            LOG.info("Transcription job completed: %s", job_name)
        except Exception as exc:
            job["FailureReason"] = failure_reason or str(exc)
            job["TranscriptionJobStatus"] = TranscriptionJobStatus.FAILED
            LOG.exception("Transcription job %s failed: %s", job_name, job["FailureReason"])