Persistent UserWarning about KMeans Memory Leak on Windows Despite Applying Suggested Fixes

### Describe the bug

Issue Description
When running code involving GaussianMixture (or KMeans), a UserWarning about a known memory leak on Windows with MKL is raised, even after implementing the suggested workaround (OMP_NUM_THREADS=1 or 2). The warning persists across multiple environments and configurations, indicating the issue may require further investigation.

Warning Message:

```
C:\ProgramData\anaconda3\Lib\site-packages\sklearn\cluster_kmeans.py:1429: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=2.
warnings.warn(
```

Steps to Reproduce

1-Code Example:

```python
import os
os.environ["OMP_NUM_THREADS"] = "1" # Also tested with "2"
os.environ["MKL_NUM_THREADS"] = "1"

import numpy as np
from sklearn.datasets import make_blobs
from sklearn.mixture import GaussianMixture

# Generate synthetic 3D data
X, _ = make_blobs(n_samples=300, n_features=3, centers=3, random_state=42)

# Train GMM model
gmm = GaussianMixture(n_components=3, random_state=42)
gmm.fit(X) # Warning triggered here
```

## Environment:

OS: Windows 11
Python: 3.10.12
scikit-learn: 1.3.2
numpy: 1.26.0 (linked to MKL via Anaconda)
Installation Method: Anaconda (conda install scikit-learn).

## Expected vs. Actual Behavior
Expected: Setting OMP_NUM_THREADS should suppress the warning and resolve the memory leak.

Actual: The warning persists despite environment variable configurations, reinstalls, and thread-limiting methods.

## Attempted Fixes

Set OMP_NUM_THREADS=1 or 2 in code and system environment variables.
Limited threads via threadpoolctl:
code:
```python
from threadpoolctl import threadpool_limits
with threadpool_limits(limits=1, user_api='blas'):
gmm.fit(X)
```

Reinstalled numpy and scipy with OpenBLAS instead of MKL.
Tested in fresh conda environments.
Updated all packages to latest versions.
None of these resolved the warning.

Additional Context:
The warning appears even when using GaussianMixture, which indirectly relies on KMeans-related code.

The issue is specific to Windows + MKL. No warnings on Linux/Mac.

Full error log: [Attach log if available].

Questions for Maintainers:
Is there a deeper configuration or bug causing this warning to persist?
Are there alternative workarounds for Windows users?
Is this issue being tracked in ongoing development?
Thank you for your time and support!
Let me know if further details are needed.

### Steps/Code to Reproduce

```python
import os
os.environ["OMP_NUM_THREADS"] = "1"  # Also tested with "2"
os.environ["MKL_NUM_THREADS"] = "1"

import numpy as np
from sklearn.datasets import make_blobs
from sklearn.mixture import GaussianMixture

# Generate synthetic 3D data
X, _ = make_blobs(n_samples=300, n_features=3, centers=3, random_state=42)

# Train GMM model
gmm = GaussianMixture(n_components=3, random_state=42)
gmm.fit(X)  # Warning triggered here
```

### Expected Results

```
C:\ProgramData\anaconda3\Lib\site-packages\sklearn\cluster\_kmeans.py:1429: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=2.
  warnings.warn(
```

### Actual Results

```
C:\ProgramData\anaconda3\Lib\site-packages\sklearn\cluster\_kmeans.py:1429: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=2.
  warnings.warn(
```


### Versions

```shell
scikit-learn: 1.3.2

numpy: 1.26.0 (linked to MKL via Anaconda)
```

COMMENT:
@jeremiedbb Thank you for your suggestion. The warning has been suppressed. Here's an updated reproducer and output:

I have one question: the `threadpool_limit` is used in a with loop. Does this mean we have to keep every kmeans reference in one loop or set it dynamically around every occurrence?

```python
import numpy as np
from sklearn.cluster import KMeans
import os

def reproduce_openmp_warning():
    """
    Minimal demo to reproduce OMP_NUM_THREADS warning.
    
    The warning occurs because we're trying to set OMP_NUM_THREADS
    after scikit-learn has already initialized OpenMP.
    """
    
    # Generate some dummy data
    data = np.random.randn(1000, 1)
    
    # First, use KMeans (this initializes OpenMP)
    print("Running KMeans (this initializes OpenMP)...")
    kmeans = KMeans(n_clusters=3, random_state=0, n_init=10).fit(data)
    print(f"Found {len(kmeans.cluster_centers_)} clusters")
    
    # Now try to set OMP_NUM_THREADS (this should trigger the warning)
    print("\nTrying to set OMP_NUM_THREADS with os.environ after OpenMP initialization...")
    os.environ["OMP_NUM_THREADS"] = "6"
    print("OMP_NUM_THREADS set to 6")
    
    # Run KMeans again to see if the warning appears
    print("\nRunning KMeans again...")
    kmeans2 = KMeans(n_clusters=5, random_state=0, n_init=10).fit(data)
    print(f"Found {len(kmeans2.cluster_centers_)} clusters")

def reproduce_openmp_warning_fixed():
    print("\n" + "="*50)
    print("FIXED VERSION:")
    print("="*50)
    
    
    # Generate dummy data
    data = np.random.randn(1000, 1)
    
    print("Running KMeans...")
    from threadpoolctl import threadpool_limits
    with threadpool_limits(user_api="openmp", limits=4):
        kmeans = KMeans(n_clusters=3, random_state=0, n_init=10).fit(data)
    print(f"Found {len(kmeans.cluster_centers_)} clusters")

if __name__ == "__main__":
    print("Demonstrating OMP_NUM_THREADS warning...")
    reproduce_openmp_warning()
    reproduce_openmp_warning_fixed()
```

Output with dynamic threadpool limit fix:
```
Demonstrating OMP_NUM_THREADS warning...
Running KMeans (this initializes OpenMP)...
C:\Users\user\miniconda3\envs\ns01-python-3.11\Lib\site-packages\sklearn\cluster\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=4.
  warnings.warn(
Found 3 clusters

Trying to set OMP_NUM_THREADS with os.environ after OpenMP initialization...
OMP_NUM_THREADS set to 6

Running KMeans again...
C:\Users\user\miniconda3\envs\ns01-python-3.11\Lib\site-packages\sklearn\cluster\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=4.
  warnings.warn(
Found 5 clusters

==================================================
FIXED VERSION:
==================================================
Running KMeans...
Found 3 clusters
```

Labels: Bug, Needs Info