SequentialFeatureSelector fails on text features even though the estimator supports them

### Describe the bug

When a model can handle the data type (may it be text or NaN), `SequentialFeatureSelector` appears to be performing its own validation ignoring the capability of the model and apparently always insists that everything must be numbers. `cross_val_score` appears to be working so it's `SequentialFeatureSelector` that is rejecting the data.

### Steps/Code to Reproduce

```python
from sklearn.datasets import load_diabetes
from sklearn.feature_selection import SequentialFeatureSelector
from xgboost import XGBRegressor
from sklearn.model_selection import cross_val_score

import sklearn; print(F'{sklearn.__version__=}')
import xgboost; print(F'{xgboost.__version__=}')

X, y = load_diabetes(return_X_y=True, as_frame=True, scaled=False)
X['sex'] = X['sex'].apply(lambda x: 'M' if x==1.0 else 'F').astype('category')
model = XGBRegressor(enable_categorical=True, random_state=0)
print('Testing cross_val_score begins')
cross_val_score(model, X, y, error_score='raise') # no error
print('Testing cross_val_score ends')
print('Testing SequentialFeatureSelector begins')
SequentialFeatureSelector(model, tol=0).fit(X, y)
print('Testing SequentialFeatureSelector ends')
```

### Expected Results

```text
sklearn.__version__='1.6.1'
xgboost.__version__='2.1.4'
Testing cross_val_score begins
Testing cross_val_score ends
Testing SequentialFeatureSelector begins
Testing SequentialFeatureSelector ends
```
(No errors)

### Actual Results

```text
sklearn.__version__='1.6.1'
xgboost.__version__='2.1.4'
Testing cross_val_score begins
Testing cross_val_score ends
Testing SequentialFeatureSelector begins

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-29-fb1642c5f9e7> in <cell line: 16>()
     14 print('Testing cross_val_score ends')
     15 print('Testing SequentialFeatureSelector begins')
---> 16 SequentialFeatureSelector(model, tol=0).fit(X, y)
     17 print('Testing SequentialFeatureSelector ends')

/usr/local/lib/python3.10/dist-packages/sklearn/base.py in wrapper(estimator, *args, **kwargs)
   1387                 )
   1388             ):
-> 1389                 return fit_method(estimator, *args, **kwargs)
   1390 
   1391         return wrapper

/usr/local/lib/python3.10/dist-packages/sklearn/feature_selection/_sequential.py in fit(self, X, y, **params)
    280             process_routing(self, "fit", **params)
    281         for _ in range(n_iterations):
--> 282             new_feature_idx, new_score = self._get_best_new_feature_score(
    283                 cloned_estimator, X, y, cv, current_mask, **params
    284             )

/usr/local/lib/python3.10/dist-packages/sklearn/feature_selection/_sequential.py in _get_best_new_feature_score(self, estimator, X, y, cv, current_mask, **params)
    311                 candidate_mask = ~candidate_mask
    312             X_new = X[:, candidate_mask]
--> 313             scores[feature_idx] = cross_val_score(
    314                 estimator,
    315                 X_new,

/usr/local/lib/python3.10/dist-packages/sklearn/utils/_param_validation.py in wrapper(*args, **kwargs)
    214                     )
    215                 ):
--> 216                     return func(*args, **kwargs)
    217             except InvalidParameterError as e:
    218                 # When the function is just a wrapper around an estimator, we allow

/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py in cross_val_score(estimator, X, y, groups, scoring, cv, n_jobs, verbose, params, pre_dispatch, error_score)
    682     scorer = check_scoring(estimator, scoring=scoring)
    683 
--> 684     cv_results = cross_validate(
    685         estimator=estimator,
    686         X=X,

/usr/local/lib/python3.10/dist-packages/sklearn/utils/_param_validation.py in wrapper(*args, **kwargs)
    214                     )
    215                 ):
--> 216                     return func(*args, **kwargs)
    217             except InvalidParameterError as e:
    218                 # When the function is just a wrapper around an estimator, we allow

/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py in cross_validate(estimator, X, y, groups, scoring, cv, n_jobs, verbose, params, pre_dispatch, return_train_score, return_estimator, return_indices, error_score)
    429     )
    430 
--> 431     _warn_or_raise_about_fit_failures(results, error_score)
    432 
    433     # For callable scoring, the return type is only know after calling. If the

/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py in _warn_or_raise_about_fit_failures(results, error_score)
    515                 f"Below are more details about the failures:\n{fit_errors_summary}"
    516             )
--> 517             raise ValueError(all_fits_failed_message)
    518 
    519         else:

ValueError: 
All the 5 fits failed.
It is very likely that your model is misconfigured.
You can try to debug the error by setting error_score='raise'.

Below are more details about the failures:
--------------------------------------------------------------------------------
1 fits failed with the following error:
Traceback (most recent call last):
  File "/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py", line 866, in _fit_and_score
    estimator.fit(X_train, y_train, **fit_params)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 1143, in fit
    train_dmatrix, evals = _wrap_evaluation_matrices(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 603, in _wrap_evaluation_matrices
    train_dmatrix = create_dmatrix(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 1065, in _create_dmatrix
    return QuantileDMatrix(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 1573, in __init__
    self._init(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 1632, in _init
    it.reraise()
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 569, in reraise
    raise exc  # pylint: disable=raising-bad-type
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 550, in _handle_exception
    return fn()
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 637, in <lambda>
    return self._handle_exception(lambda: self.next(input_data), 0)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 1402, in next
    input_data(**self.kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 617, in input_data
    new, cat_codes, feature_names, feature_types = _proxy_transform(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 1429, in _proxy_transform
    data, _ = _ensure_np_dtype(data, data.dtype)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 224, in _ensure_np_dtype
    data = data.astype(dtype, copy=False)
ValueError: could not convert string to float: 'M'

--------------------------------------------------------------------------------
4 fits failed with the following error:
Traceback (most recent call last):
  File "/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py", line 866, in _fit_and_score
    estimator.fit(X_train, y_train, **fit_params)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 1143, in fit
    train_dmatrix, evals = _wrap_evaluation_matrices(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 603, in _wrap_evaluation_matrices
    train_dmatrix = create_dmatrix(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/sklearn.py", line 1065, in _create_dmatrix
    return QuantileDMatrix(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 1573, in __init__
    self._init(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 1632, in _init
    it.reraise()
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 569, in reraise
    raise exc  # pylint: disable=raising-bad-type
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 550, in _handle_exception
    return fn()
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 637, in <lambda>
    return self._handle_exception(lambda: self.next(input_data), 0)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 1402, in next
    input_data(**self.kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 726, in inner_f
    return func(**kwargs)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/core.py", line 617, in input_data
    new, cat_codes, feature_names, feature_types = _proxy_transform(
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 1429, in _proxy_transform
    data, _ = _ensure_np_dtype(data, data.dtype)
  File "/usr/local/lib/python3.10/dist-packages/xgboost/data.py", line 224, in _ensure_np_dtype
    data = data.astype(dtype, copy=False)
ValueError: could not convert string to float: 'F'
```

### Versions

```shell
Python dependencies:
      sklearn: 1.6.1
          pip: 24.1.2
   setuptools: 75.1.0
        numpy: 1.26.4
        scipy: 1.13.1
       Cython: 3.0.11
       pandas: 2.2.2
   matplotlib: 3.7.5
       joblib: 1.4.2
threadpoolctl: 3.5.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: mkl
    num_threads: 2
         prefix: libmkl_rt
       filepath: /usr/local/lib/libmkl_rt.so.2
        version: 2025.0.1-Product
threading_layer: gnu

       user_api: blas
   internal_api: mkl
    num_threads: 2
         prefix: libmkl_rt
       filepath: /usr/local/lib/python3.10/dist-packages/mkl_fft.libs/libmkl_rt-089e6a60.so.2
        version: 2025.0.1-Product
threading_layer: not specified

       user_api: openmp
   internal_api: openmp
    num_threads: 4
         prefix: libgomp
       filepath: /usr/lib/x86_64-linux-gnu/libgomp.so.1.0.0
        version: None

       user_api: blas
   internal_api: openblas
    num_threads: 4
         prefix: libopenblas
       filepath: /usr/local/lib/python3.10/dist-packages/scipy.libs/libopenblasp-r0-01191904.3.27.so
        version: 0.3.27
threading_layer: pthreads
   architecture: Haswell

       user_api: openmp
   internal_api: openmp
    num_threads: 4
         prefix: libgomp
       filepath: /usr/local/lib/python3.10/dist-packages/scikit_learn.libs/libgomp-a34b3233.so.1.0.0
        version: None

       user_api: openmp
   internal_api: openmp
    num_threads: 4
         prefix: libgomp
       filepath: /usr/local/lib/python3.10/dist-packages/xgboost.libs/libgomp-24e2ab19.so.1.0.0
        version: None
```

COMMENT:
@adrinjalali Looking at the traceback dump, it would appear that `SequentialFeatureSelector` had converted the original pandas dataframe `X` into a numpy array (perhaps via `check_X_y` somewhere; you can tell from code like `X_new = X[:, candidate_mask]` that `X` was not a pandas dataframe), which supports only one `dtype`, which in this case would have to be `object`. xgboost was trying to recover by converting the values to float but failed.

It may be tied too deeply into the architectural design of `SequentialFeatureSelector` but to support mixed `dtype`'s for a feature matrix, numpy arrays are not the right choice.

Labels: Bug, Needs Investigation