is_classifier() returns False for Custom Classifier

### Describe the bug

`is_classifier()` should return True for an instance of a custom classifier.

### Steps/Code to Reproduce

```python
from sklearn.base import BaseEstimator, ClassifierMixin, is_classifier
from sklearn import __version__ as sklearn_version

# A minimal estimator class inheriting from both.

class MyClassifier(BaseEstimator, ClassifierMixin):
    def fit(self, X, y):
        return self

    def predict(self, X):
        return [1] * len(X)

# 1. Instantiate the estimator
my_clf = MyClassifier()

# 2. Check its type using the function
is_it_a_classifier = is_classifier(my_clf)

print(f"Is `my_clf` a classifier? -> {is_it_a_classifier}")
print(f"Version of sklearn: {sklearn_version}")
```

### Expected Results

Should return True.

### Actual Results

Returns False.

### Versions

```shell
System:
    python: 3.11.14 | packaged by conda-forge | (main, Oct 13 2025, 14:00:26) [MSC v.1944 64 bit (AMD64)]
executable: c:\Users\william.chiu\.conda\envs\env_sklearnex_202510\python.exe
   machine: Windows-10-10.0.17763-SP0

Python dependencies:
      sklearn: 1.7.2
          pip: 25.2
   setuptools: 80.9.0
        numpy: 2.1.3
        scipy: 1.15.3
       Cython: 3.1.4
       pandas: 2.3.3
   matplotlib: 3.10.0
       joblib: 1.5.2
threadpoolctl: 3.6.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
    num_threads: 72
         prefix: vcomp
       filepath: C:\Users\william.chiu\.conda\envs\env_sklearnex_202510\Lib\site-packages\sklearn\.libs\vcomp140.dll
        version: None

       user_api: blas
   internal_api: openblas
    num_threads: 24
         prefix: libscipy_openblas
       filepath: C:\Users\william.chiu\.conda\envs\env_sklearnex_202510\Lib\site-packages\numpy.libs\libscipy_openblas64_-c16e4918366c6bc1f1cd71e28ca36fc0.dll
        version: 0.3.27
threading_layer: pthreads
   architecture: SkylakeX

       user_api: blas
   internal_api: openblas
    num_threads: 24
         prefix: libscipy_openblas
       filepath: C:\Users\william.chiu\.conda\envs\env_sklearnex_202510\Lib\site-packages\scipy.libs\libscipy_openblas-f07f5a5d207a3a47104dca54d6d0c86a.dll
        version: 0.3.28
threading_layer: pthreads
   architecture: SkylakeX
```

COMMENT:
Please close the issue. The [documentation ](https://scikit-learn.org/stable/developers/develop.html )says to inherit `ClassifierMixin` before inheriting `BaseEstimator`.

The code below returns True:

```python
from sklearn.base import BaseEstimator, ClassifierMixin, is_classifier
from sklearn import __version__ as sklearn_version

# A minimal estimator class inheriting from both.

class MyClassifier(ClassifierMixin, BaseEstimator):  # order matters
    def fit(self, X, y):
        return self

    def predict(self, X):
        return [1] * len(X)

# 1. Instantiate the estimator
my_clf = MyClassifier()

# 2. Check its type using the function
is_it_a_classifier = is_classifier(my_clf)

print(f"Is `my_clf` a classifier? -> {is_it_a_classifier}")
print(f"Version of sklearn: {sklearn_version}")
```

Output:

```
Is `my_clf` a classifier? -> True
Version of sklearn: 1.7.2
```

Labels: Bug, Needs Triage