`Permission denied` when sharing cache between users

### Describe the bug

We want to use `datasets` and `transformers` on a shared machine. Right now, each user has a separate HF_HOME in their home directory. To reduce duplicates of the datasets, we want to share that cache. While experimenting, we are running into `Permission denied` errors.

It looks like this was supported in the past (see #6589)?

Is there a correct way to share caches across users?

### Steps to reproduce the bug

1. Create a directory `/models/hf_hub_shared_experiment` with read/write permissions for two different users
2. For each user run the script below

```python
import os

os.environ["HF_HOME"] = "/models/hf_hub_shared_experiment"
os.environ["HF_DATASETS_CACHE"] = "/models/hf_hub_shared_experiment/data"

import datasets
import transformers

DATASET = "tatsu-lab/alpaca"
MODEL = "meta-llama/Llama-3.2-1B-Instruct"

model = transformers.AutoModelForCausalLM.from_pretrained(MODEL)
tokenizer = transformers.AutoTokenizer.from_pretrained(MODEL)
dataset = datasets.load_dataset(DATASET)
```

The first user is able to download and use the model and dataset. The second user gets these errors:

```
$ python ./experiment_with_shared.py
Could not cache non-existence of file. Will ignore error and continue. Error: [Errno 13] Permission denied: '/models/hf_hub_shared_experiment/hub/models--meta-llama--Llama-3.2-1B-Instruct/.no_exist/9213176726f574b556790deb65791e0c5aa438b6/custom_generate/generate.py'
Could not cache non-existence of file. Will ignore error and continue. Error: [Errno 13] Permission denied: '/models/hf_hub_shared_experiment/hub/datasets--tatsu-lab--alpaca/.no_exist/dce01c9b08f87459cf36a430d809084718273017/alpaca.py'
Could not cache non-existence of file. Will ignore error and continue. Error: [Errno 13] Permission denied: '/models/hf_hub_shared_experiment/hub/datasets--tatsu-lab--alpaca/.no_exist/dce01c9b08f87459cf36a430d809084718273017/.huggingface.yaml'
Could not cache non-existence of file. Will ignore error and continue. Error: [Errno 13] Permission denied: '/models/hf_hub_shared_experiment/hub/datasets--tatsu-lab--alpaca/.no_exist/dce01c9b08f87459cf36a430d809084718273017/dataset_infos.json'
Traceback (most recent call last):
File "/home/user2/.venv/experiment_with_shared.py", line 17, in
dataset = datasets.load_dataset(DATASET)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/user2/.venv/lib/python3.12/site-packages/datasets/load.py", line 1397, in load_dataset
builder_instance = load_dataset_builder(
^^^^^^^^^^^^^^^^^^^^^
File "/home/user2/.venv/lib/python3.12/site-packages/datasets/load.py", line 1171, in load_dataset_builder
builder_instance: DatasetBuilder = builder_cls(
^^^^^^^^^^^^
File "/home/user2/.venv/lib/python3.12/site-packages/datasets/builder.py", line 390, in __init__
with FileLock(lock_path):
File "/home/user2/.venv/lib/python3.12/site-packages/filelock/_api.py", line 377, in __enter__
self.acquire()
File "/home/user2/.venv/lib/python3.12/site-packages/filelock/_api.py", line 333, in acquire
self._acquire()
File "/home/user2/.venv/lib/python3.12/site-packages/filelock/_unix.py", line 45, in _acquire
fd = os.open(self.lock_file, open_flags, self._context.mode)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
PermissionError: [Errno 13] Permission denied: '/models/hf_hub_shared_experiment/data/_models_hf_hub_shared_experiment_data_tatsu-lab___alpaca_default_0.0.0_dce01c9b08f87459cf36a430d809084718273017.lock'
```

### Expected behavior

The second user should be able to read the shared cache files.

### Environment info

$ datasets-cli env

- `datasets` version: 4.4.1
- Platform: Linux-6.8.0-88-generic-x86_64-with-glibc2.39
- Python version: 3.12.3
- `huggingface_hub` version: 0.36.0
- PyArrow version: 22.0.0
- Pandas version: 2.3.3
- `fsspec` version: 2025.10.0