### 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_
store, job_name = args
        job = store.transcription_jobs[job_name]
        job["StartTime"] = datetime.datetime.utcnow()
        job["TranscriptionJobStatus"] = TranscriptionJobStatus.IN_PROGRESS
        failure_reason = None
        try:
            LOG.debug("Starting transcription: %s", job_name)
            
            file_path = new_tmp_file()
            s3_client = aws_stack.connect_to_service("s3")
            s3_path = job["Media"]["MediaFileUri"]
            bucket, _, key = s3_path.removeprefix("s3://").partition("/")
            s3_client.download_file(Bucket=bucket, Key=key, Filename=file_path)
            ffmpeg_bin = ffmpeg_package.get_installer().get_ffmpeg_path()
            ffprobe_bin = ffmpeg_package.get_installer().get_ffprobe_path()
            LOG.debug("Determining media format")
            
            ffprobe_output = json.loads(