StreamingDataset not working in multi-gpu environement

### Bug description

I'm trying to use the Streaming library by Mosaic as described in the doc (https://lightning.ai/docs/pytorch/stable/data/alternatives.html) but it doesn't work as seamlessly as expected.

When trying the default approach as described in the documentation with 4 GPUs on a single node:
```
train_dataset = YourDataset()
train_dataloader = DataLoader(train_dataset, batch_size=batch_size)
model = ...
trainer = L.Trainer()
trainer.fit(model, train_dataloader)
```
results in the following error:
```
FileExistsError: [Errno 17] File exists: '/000001_locals'
```

Mu understanding is that the environment variables (WORLD_SIZE, LOCAL_WORLD_SIZE, RANK, etc) are not set properly in time and thus the StreamingDataset does not know it is running in a multi-gpu/multi-node and thus the different processes are unaware of each others.

You can create the dataset after the trainer, but it does not change the outcome.

Has anyone been successful in running Streaming with lightning in a multi-node/multi-gpu setup?

### What version are you seeing the problem on?

v2.2

### How to reproduce the bug

_No response_

### Error messages and logs

_No response_

### Environment

Current environment

* CUDA:
- GPU: None
- available: False
- version: 12.1
* Lightning:
- ema-pytorch: 0.4.2
- lightning: 2.2.4
- lightning-utilities: 0.10.1
- pytorch-lightning: 2.2.1
- torch: 2.2.1
- torchinfo: 1.8.0
- torchmetrics: 1.3.0.post0
- torchvision: 0.17.1
* Packages:
- absl-py: 2.1.0
- accelerate: 0.28.0
- aiohttp: 3.9.1
- aiosignal: 1.3.1
- antlr4-python3-runtime: 4.9.3
- appdirs: 1.4.4
- async-timeout: 4.0.3
- attrs: 23.2.0
- azure-core: 1.30.2
- azure-identity: 1.17.1
- azure-storage-blob: 12.21.0
- azure-storage-file-datalake: 12.16.0
- bcrypt: 4.2.0
- beartype: 0.17.2
- boto3: 1.34.149
- botocore: 1.34.149
- brotli: 1.1.0
- cachetools: 5.3.2
- certifi: 2023.11.17
- cffi: 1.16.0
- charset-normalizer: 3.3.2
- circuitbreaker: 1.4.0
- click: 8.1.7
- configparser: 6.0.0
- consistencydecoder: 1.0
- contourpy: 1.2.1
- cramjam: 2.8.3
- cryptography: 42.0.8
- cycler: 0.12.1
- diffusers: 0.27.0
- docker-pycreds: 0.4.0
- einops: 0.7.0
- ema-pytorch: 0.4.2
- filelock: 3.13.1
- fonttools: 4.53.1
- frozenlist: 1.4.1
- fsspec: 2023.12.2
- gitdb: 4.0.11
- gitpython: 3.1.41
- google-api-core: 2.19.1
- google-auth: 2.26.2
- google-auth-oauthlib: 1.2.0
- google-cloud-core: 2.4.1
- google-cloud-storage: 2.10.0
- google-crc32c: 1.5.0
- google-resumable-media: 2.7.1
- googleapis-common-protos: 1.63.2
- grpcio: 1.60.0
- huggingface-hub: 0.21.4
- hydra-core: 1.3.2
- idna: 3.6
- importlib-metadata: 7.0.2
- isodate: 0.6.1
- jinja2: 3.1.3
- jmespath: 1.0.1
- kiwisolver: 1.4.5
- lightning: 2.2.4
- lightning-utilities: 0.10.1
- lsuv: 0.2.2
- markdown: 3.5.2
- markupsafe: 2.1.3
- matplotlib: 3.9.1
- mosaicml-streaming: 0.7.6
- mpmath: 1.3.0
- msal: 1.30.0
- msal-extensions: 1.2.0
- multidict: 6.0.4
- networkx: 3.2.1
- numpy: 1.26.3
- nvidia-cublas-cu12: 12.1.3.1
- nvidia-cuda-cupti-cu12: 12.1.105
- nvidia-cuda-nvrtc-cu12: 12.1.105
- nvidia-cuda-runtime-cu12: 12.1.105
- nvidia-cudnn-cu12: 8.9.2.26
- nvidia-cufft-cu12: 11.0.2.54
- nvidia-curand-cu12: 10.3.2.106
- nvidia-cusolver-cu12: 11.4.5.107
- nvidia-cusparse-cu12: 12.1.0.106
- nvidia-nccl-cu12: 2.19.3
- nvidia-nvjitlink-cu12: 12.3.101
- nvidia-nvtx-cu12: 12.1.105
- oauthlib: 3.2.2
- oci: 2.129.4
- omegaconf: 2.3.0
- packaging: 23.2
- paramiko: 3.4.0
- pathtools: 0.1.2
- pillow: 10.2.0
- pip: 24.1.2
- portalocker: 2.10.1
- promise: 2.3
- proto-plus: 1.24.0
- protobuf: 4.23.4
- psutil: 5.9.7
- pyasn1: 0.5.1
- pyasn1-modules: 0.3.0
- pycparser: 2.22
- pyjwt: 2.8.0
- pynacl: 1.5.0
- pyopenssl: 24.2.1
- pyparsing: 3.1.2
- python-dateutil: 2.8.2
- python-snappy: 0.7.2
- pytorch-lightning: 2.2.1
- pytz: 2024.1
- pyyaml: 6.0.1
- regex: 2023.12.25
- requests: 2.31.0
- requests-oauthlib: 1.3.1
- rsa: 4.9
- s3transfer: 0.10.2
- safetensors: 0.4.2
- scipy: 1.12.0
- sentry-sdk: 1.39.2
- setproctitle: 1.3.3
- setuptools: 58.1.0
- shortuuid: 1.0.11
- six: 1.16.0
- smmap: 5.0.1
- subprocess32: 3.5.4
- sympy: 1.12
- tensorboard: 2.15.1
- tensorboard-data-server: 0.7.2
- termcolor: 2.4.0
- timm: 0.9.16
- tokenizers: 0.19.1
- torch: 2.2.1
- torchinfo: 1.8.0
- torchmetrics: 1.3.0.post0
- torchvision: 0.17.1
- tqdm: 4.66.1
- transformers: 4.40.2
- triton: 2.2.0
- typing-extensions: 4.9.0
- urllib3: 2.1.0
- wandb: 0.16.6
- werkzeug: 3.0.1
- xxhash: 3.4.1
- yarl: 1.9.4
- yaspin: 3.0.1
- zipp: 3.18.1
- zstd: 1.5.5.1
* System:
- OS: Linux
- architecture:
- 64bit
- ELF
- processor: x86_64
- python: 3.10.4
- release: 5.14.0-284.55.1.el9_2.x86_64
- version: #1 SMP PREEMPT_DYNAMIC Mon Feb 19 16:57:59 EST 2024

### More info

_No response_

Start with the documented StreamingDataset example, DataLoader, and Trainer.fit flow shown in the issue, then reproduce it with four GPUs and the listed package versions. Done means the multi-GPU run completes without the FileExistsError and the dataset processes are aware of the distributed environment.

Written by the indexing model from the issue text.