Kernel crash on BayesianGaussianMixture

### Describe the bug

I learn BayesianGaussianMixture right now and get kernel crash on sklearn documentation example.
The error is 100% reproducible and wont go away after OS restrat, kernel restrat. I even try to read Goodfellow, no effect.

Initially i got the error on version chosen by `conda install scikit-learn` but then i tried to upgrade to `conda install scikit-learn==1.8.0` (pkgs/main::scikit-learn-1.7.1-py311h3~ --> conda-forge::scikit-learn-1.8.0-np2py311hd01f973_1) but got the same error.

### Steps/Code to Reproduce

import numpy as np
from sklearn.mixture import BayesianGaussianMixture
from sklearn import show_versions
print(np.__version__)
print(show_versions())
X = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [12, 4], [10, 7]])
bgm = BayesianGaussianMixture(n_components=2, random_state=42).fit(X)

### Expected Results

I dont know since I never managed to run the code

### Actual Results

2.0.1

System:
    python: 3.11.13 | packaged by Anaconda, Inc. | (main, Jun  5 2025, 13:03:15) [MSC v.1929 64 bit (AMD64)]
executable: [c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\python.exe](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/python.exe)
   machine: Windows-10-10.0.19045-SP0

Python dependencies:
      sklearn: 1.8.0
          pip: 25.2
   setuptools: 80.9.0
        numpy: 2.0.1
        scipy: 1.16.0
       Cython: None
       pandas: 2.3.3
   matplotlib: 3.10.7
       joblib: 1.5.2
threadpoolctl: 3.5.0

Built with OpenMP: True
---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
Cell In[4], [line 5](vscode-notebook-cell:?execution_count=4&line=5)
      3 from sklearn import show_versions
      4 print(np.__version__)
----> [5](vscode-notebook-cell:?execution_count=4&line=5) print(show_versions())
      6 X = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [12, 4], [10, 7]])
      7 bgm = BayesianGaussianMixture(n_components=2, random_state=42).fit(X)

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\sklearn\utils\_show_versions.py:106, in show_versions()
     99 print(
    100     "\n{k}: {stat}".format(
    101         k="Built with OpenMP", stat=_openmp_parallelism_enabled()
    102     )
    103 )
    105 # show threadpoolctl results
--> [106](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/sklearn/utils/_show_versions.py:106) threadpool_results = threadpool_info()
    107 if threadpool_results:
    108     print()

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:567, in threadpool_info()
    551 @_format_docstring(USER_APIS=list(_ALL_USER_APIS), INTERNAL_APIS=_ALL_INTERNAL_APIS)
    552 def threadpool_info():
    553     """Return the maximal number of threads for each detected library.
    554 
    555     Return a list with all the supported libraries that have been found. Each
   (...)    565     In addition, each library may contain internal_api specific entries.
    566     """
--> [567](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:567)     return ThreadpoolController().info()

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:829, in ThreadpoolController.info(self)
    827 def info(self):
    828     """Return lib_controllers info as a list of dicts"""
--> [829](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:829)     return [lib_controller.info() for lib_controller in self.lib_controllers]

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:829, in <listcomp>(.0)
    827 def info(self):
    828     """Return lib_controllers info as a list of dicts"""
--> [829](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:829)     return [lib_controller.info() for lib_controller in self.lib_controllers]

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:125, in LibController.info(self)
    120 """Return relevant info wrapped in a dict"""
    121 hidden_attrs = ("dynlib", "parent", "_symbol_prefix", "_symbol_suffix")
    122 return {
    123     "user_api": self.user_api,
    124     "internal_api": self.internal_api,
--> [125](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:125)     "num_threads": self.num_threads,
    126     **{k: v for k, v in vars(self).items() if k not in hidden_attrs},
    127 }

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:138, in LibController.num_threads(self)
    132 @property
    133 def num_threads(self):
    134     """Exposes the current thread limit as a dynamic property
    135 
    136     This is not meant to be used or overriden by subclasses.
    137     """
--> [138](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:138)     return self.get_num_threads()

File c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\Lib\site-packages\threadpoolctl.py:444, in MKLController.get_num_threads(self)
    442 def get_num_threads(self):
    443     get_func = getattr(self.dynlib, "MKL_Get_Max_Threads", lambda: None)
--> [444](file:///C:/Users/my_user/AppData/Local/anaconda3/envs/vdl/Lib/site-packages/threadpoolctl.py:444)     return get_func()

OSError: [WinError -1066598274] Windows Error 0xc06d007e

### Versions

```shell
System:
    python: 3.11.13 | packaged by Anaconda, Inc. | (main, Jun  5 2025, 13:03:15) [MSC v.1929 64 bit (AMD64)]
executable: c:\Users\my_user\AppData\Local\anaconda3\envs\vdl\python.exe
   machine: Windows-10-10.0.19045-SP0

Python dependencies:
      sklearn: 1.8.0
          pip: 25.2
   setuptools: 80.9.0
        numpy: 2.0.1
        scipy: 1.16.0
       Cython: None
       pandas: 2.3.3
   matplotlib: 3.10.7
       joblib: 1.5.2
threadpoolctl: 3.5.0

Built with OpenMP: True
```

COMMENT:
I have just noticed that error above come from show_versions() and not from BayesianGaussianMixture. But initially i was investigating  another problem:

The code:
```
import numpy as np
from sklearn.mixture import BayesianGaussianMixture
import sklearn
import time
print(f"{np.__version__=}")
print(f"{sklearn.__version__=}")
# print(show_versions())
X = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [12, 4], [10, 7]])
print(f"{X=}")
time.sleep(3)
bgm = BayesianGaussianMixture().fit(X)
```

Result:
```
np.__version__='2.0.1'
sklearn.__version__='1.8.0'
X=array([[ 1,  2],
       [ 1,  4],
       [ 1,  0],
       [ 4,  2],
       [12,  4],
       [10,  7]])
The Kernel crashed while executing code in the current cell or a previous cell. 
Please review the code in the cell(s) to identify a possible cause of the failure. 
Click [here](https://aka.ms/vscodeJupyterKernelCrash) for more info. 
View Jupyter [log](command:jupyter.viewOutput) for further details.
```

I have added `time.sleep(3)` to get first prints. If there is no delay, kernel crashes before print results are visible.

Jupyter logs (i've restarted kernel manually)
```
08:52:15.751 [info] Restart requested Untitled-1.ipynb
08:52:15.755 [warn] Cancel all remaining cells due to dead kernel
08:52:20.797 [info] Process Execution: ~\AppData\Local\anaconda3\envs\vdl\python.exe -c "import ipykernel; print(ipykernel.__version__); print("5dc3a68c-e34e-4080-9c3e-2a532b2ccb4d"); print(ipykernel.__file__)"
08:52:20.821 [info] Process Execution: ~\AppData\Local\anaconda3\envs\vdl\python.exe -m ipykernel_launcher --f=~\AppData\Roaming\jupyter\runtime\kernel-v3d2ce0e1f723a8cd305459473d3e48e61da7aad10.json
    > cwd: ~\AppData\Local\Programs\Microsoft VS Code
08:52:22.037 [info] Restarted 01921a56-4b4b-4285-b69b-f178b230db16
08:52:37.651 [error] Disposing session as kernel process died ExitCode: 3228369022, Reason: 
```

Labels: Bug, Needs Triage