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:
Thank you for your reply. I updated to 1.7.1 and the same error occurred.
The installation is from pip rather than conda.

I tried on the generated code below, which can reproduce the error on my machine. I also put on my sklearn.show_versions() at the end: 

**Expected behavior and actual behavior:**

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

def reproduce_omp_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 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_omp_warning_fixed():
    """
    Fixed version: Set OMP_NUM_THREADS before importing sklearn
    """
    print("\n" + "="*50)
    print("FIXED VERSION:")
    print("="*50)
    print("Setting OMP_NUM_THREADS before using OpenMP libraries...")
    
    # Generate dummy data
    data = np.random.randn(1000, 1)
    
    # Now use KMeans - should work without warnings
    print("Running KMeans...")
    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_omp_warning()
    reproduce_omp_warning_fixed()

```

Output:
```
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 after OpenMP initialization...
OMP_NUM_THREADS set to 6

Running KMeans again...
C:\Users\gn022\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:
==================================================
Setting OMP_NUM_THREADS before using OpenMP libraries...
Running KMeans...
C:\Users\gn022\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

```

sklearn.show_versions()

```
System:
    python: 3.11.9 | packaged by Anaconda, Inc. | (main, Apr 19 2024, 16:40:41) [MSC v.1916 64 bit (AMD64)]
    executable: C:\Users\gn022\miniconda3\envs\ns01-python-3.11\python.exe
    machine: Windows-10-10.0.26100-SP0

Python dependencies:
      sklearn: 1.7.1
          pip: 24.0
   setuptools: 65.6.3
        numpy: 1.26.4
        scipy: 1.13.0
       Cython: None
       pandas: 2.0.3
   matplotlib: 3.8.4
       joblib: 1.4.2
threadpoolctl: 3.5.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
    num_threads: 8
         prefix: vcomp
       filepath: C:\Users\user\miniconda3\envs\ns01-python-3.11\Lib\site-packages\sklearn\.libs\vcomp140.dll
        version: None

       user_api: blas
   internal_api: mkl
    num_threads: 8
         prefix: libblas
       filepath: C:\Users\user\miniconda3\envs\ns01-python-3.11\Library\bin\libblas.dll
        version: 2024.1-Product
threading_layer: intel

       user_api: blas
   internal_api: openblas
    num_threads: 8
         prefix: libopenblas
       filepath: C:\Users\user\miniconda3\envs\ns01-python-3.11\Lib\site-packages\scipy.libs\libopenblas_v0.3.26-382-gb1e8ba50--72a863714eca5a50b38260dedc0c2f3a.dll
        version: 0.3.26.dev
threading_layer: pthreads
   architecture: Prescott
```

Labels: Bug, Needs Info