### 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_
BadRequestException,
    ConflictException,
    GetTranscriptionJobResponse,
    ListTranscriptionJobsResponse,
    MaxResults,
    MediaFormat,
    NextToken,
    NotFoundException,
    StartTranscriptionJobRequest,
    StartTranscriptionJobResponse,
    TranscribeApi,
    Transcript,
    TranscriptionJob,
    TranscriptionJobName,
    TranscriptionJobStatus,
    TranscriptionJobSummary,
)
from localstack.packages.ffmpeg import ffmpeg_package
from localstack.services.plugins import ServiceLifecycleHook
from localstack.services.s3.utils import get_bucket_and_key_from_s3_uri
from localstack.services.transcribe.models import TranscribeStore, transcribe_stores
from localstack.utils.aws import aws_stack
from localstack.utils.files import new_tmp_file
from localstack.utils.http import download
from localstack.utils.run import run
from localstack.utils.threads import start_thread
LOG = logging.getLogger(__name__)
LANGUAGE_MODELS = {
    "en-IN": "vosk-model-small-en-in-0.4",
    "en-US": "vosk-model-small-en-us-0.15",