### 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_
run(
                    f"{ffprobe_bin} -show_streams -show_format -print_format json -hide_banner -v error {file_path}"
                )
            )
            format = ffprobe_output["format"]["format_name"]
            LOG.debug(f"Media format detected as: {format}")
            job["MediaFormat"] = SUPPORTED_FORMAT_NAMES[format]
            
            if len(ffprobe_output["streams"]):
                sample_rate = ffprobe_output["streams"][0]["sample_rate"]
                job["MediaSampleRateHertz"] = int(sample_rate)
            if format in SUPPORTED_FORMAT_NAMES:
                wav_path = new_tmp_file(suffix=".wav")
                LOG.debug("Transcoding media to wav")
                
                run(
                    f"{ffmpeg_bin} -y -nostdin -loglevel quiet -i '{file_path}' -ar 16000 -ac 1 '{wav_path}'"
                )
            else:
                failure_reason = f"Unsupported media format: {format}"
                raise RuntimeError()
            
            audio = wave.open(wav_path, "rb")
            if (
                audio.getnchannels() != 1
                or audio.getsampwidth() != 2
                or audio.getcomptype() != "NONE"
            ):
                
                failure_reason = (