sklearn.utils._param_validation.InvalidParameterError: The 'zero_division' parameter of precision_score must be a float among {0.0, 1.0, nan} or a str among {'warn'}. Got nan instead

### Describe the bug

I'm trying to use `precision_score` with `np.nan` for the `zero_division`.  It's not working with `cross_val_score` but working when I do manual cross-validation with the same pairs. 

### Steps/Code to Reproduce

Here's the data files to reproduce: 
[sklearn_data.pkl.zip](https://github.com/scikit-learn/scikit-learn/files/12861719/sklearn_data.pkl.zip)


```python
# Load in data
with open("sklearn_data.pkl", "rb") as f:
    objects = pickle.load(f)


# > objects.keys()
# dict_keys(['estimator', 'X', 'y', 'scoring', 'cv', 'n_jobs'])

estimator = objects["estimator"]
X = objects["X"]
y = objects["y"]
scoring = objects["scoring"]
cv = objects["cv"]
n_jobs = objects["n_jobs"]

# > scoring
# make_scorer(precision_score, pos_label=Case_0, zero_division=nan)

# > y.unique()
# ['Control', 'Case_0']
# Categories (2, object): ['Case_0', 'Control']

# First I checked to make sure that there are both classes in all the training and validation pairs
pos_label = "Case_0"
control_label = "Control"
for index_training, index_validation in cv:
    assert y.iloc[index_training].nunique() == 2
    assert y.iloc[index_validation].nunique() == 2
    assert pos_label in y.values
    assert control_label in y.values

# If I run manually:
scores = list()
for index_training, index_validation in cv:
    estimator.fit(X.iloc[index_training], y.iloc[index_training])
    y_hat = estimator.predict(X.iloc[index_validation])
    score = precision_score(y_true = y.iloc[index_validation], y_pred=y_hat, pos_label=pos_label)
    scores.append(score)
# > print(np.mean(scores))
# 0.501156937317928

```python
# If I use cross_val_score:
cross_val_score(estimator=estimator, X=X, y=y, cv=cv, scoring=scoring, n_jobs=n_jobs
```

```pytb
/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/model_selection/_validation.py:839: UserWarning: Scoring failed. The score on this train-test partition for these parameters will be set to nan. Details: 
Traceback (most recent call last):
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 136, in __call__
    score = scorer._score(
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 355, in _score
    return self._sign * self._score_func(y_true, y_pred, **scoring_kwargs)
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 201, in wrapper
    validate_parameter_constraints(
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 95, in validate_parameter_constraints
    raise InvalidParameterError(
sklearn.utils._param_validation.InvalidParameterError: The 'zero_division' parameter of precision_score must be a float among {0.0, 1.0, nan} or a str among {'warn'}. Got nan instead.
```

### Expected Results

0.501156937317928

### Actual Results

```pytb
/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/model_selection/_validation.py:839: UserWarning: Scoring failed. The score on this train-test partition for these parameters will be set to nan. Details: 
Traceback (most recent call last):
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 136, in __call__
    score = scorer._score(
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 355, in _score
    return self._sign * self._score_func(y_true, y_pred, **scoring_kwargs)
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 201, in wrapper
    validate_parameter_constraints(
  File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 95, in validate_parameter_constraints
    raise InvalidParameterError(
sklearn.utils._param_validation.InvalidParameterError: The 'zero_division' parameter of precision_score must be a float among {0.0, 1.0, nan} or a str among {'warn'}. Got nan instead.
```

### Versions

```shell
System:
    python: 3.9.16 | packaged by conda-forge | (main, Feb  1 2023, 21:42:20)  [Clang 14.0.6 ]
executable: /Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/bin/python
   machine: macOS-13.4.1-x86_64-i386-64bit

Python dependencies:
      sklearn: 1.3.1
          pip: 22.0.3
   setuptools: 60.7.1
        numpy: 1.24.4
        scipy: 1.8.0
       Cython: 0.29.27
       pandas: 1.4.0
   matplotlib: 3.7.1
       joblib: 1.3.2
threadpoolctl: 3.1.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: /Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/libopenblasp-r0.3.18.dylib
        version: 0.3.18
threading_layer: openmp
   architecture: Haswell
    num_threads: 16

       user_api: openmp
   internal_api: openmp
         prefix: libomp
       filepath: /Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/libomp.dylib
        version: None
    num_threads: 16
```

COMMENT:
There's some strange behavior going on.

> Could you give some information regarding what is the nan values used there.

I actually used `np.nan` but it just shows as `nan` when viewing the object

This one is a little more explicit: 

```python
import pickle
from sklearn.metrics import precision_score
from sklearn.model_selection import cross_val_score

# Load in data
with open("sklearn_data.pkl", "rb") as f:
    objects = pickle.load(f)


# > objects.keys()
# dict_keys(['estimator', 'X', 'y', 'scoring', 'cv', 'n_jobs'])

estimator = objects["estimator"]
X = objects["X"]
y = objects["y"]
scoring = objects["scoring"]
cv = objects["cv"]
n_jobs = objects["n_jobs"]

# > scoring
scoring = make_scorer(precision_score, pos_label="Case_0", zero_division=np.nan)

# > y.unique()
# ['Control', 'Case_0']
# Categories (2, object): ['Case_0', 'Control']

# First I checked to make sure that there are both classes in all the training and validation pairs
pos_label = "Case_0"
control_label = "Control"
for index_training, index_validation in cv:
    assert y.iloc[index_training].nunique() == 2
    assert y.iloc[index_validation].nunique() == 2
    assert pos_label in y.values
    assert control_label in y.values

# If I run manually using precision_score function
scores = list()
for index_training, index_validation in cv:
    estimator.fit(X.iloc[index_training], y.iloc[index_training])
    y_hat = estimator.predict(X.iloc[index_validation])
    score = precision_score(y_true = y.iloc[index_validation], y_pred=y_hat, pos_label=pos_label)
    scores.append(score)
# > print(np.mean(scores))
# 0.501156937317928

# Now using the scorer
scores = list()
for index_training, index_validation in cv:
    estimator.fit(X.iloc[index_training], y.iloc[index_training])
    y_hat = estimator.predict(X.iloc[index_validation])
    # score = precision_score(y_true = y.iloc[index_validation], y_pred=y_hat, pos_label=pos_label)
    score = scoring(estimator, X=X.iloc[index_validation], y_true=y.iloc[index_validation])
    scores.append(score)
print(np.mean(scores))
# 0.501156937317928

# If I use cross_val_score:
cross_val_score(estimator=estimator, X=X, y=y, cv=cv, scoring=scoring, n_jobs=n_jobs)
# Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/model_selection/_validation.py:839: UserWarning: Scoring failed. The score on this train-test partition for these parameters will be set to nan. Details: 
# Traceback (most recent call last):
#   File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 136, in __call__
#     score = scorer._score(
#   File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/metrics/_scorer.py", line 355, in _score
#     return self._sign * self._score_func(y_true, y_pred, **scoring_kwargs)
#   File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 201, in wrapper
#     validate_parameter_constraints(
#   File "/Users/jespinoz/anaconda3/envs/soothsayer_py3.9_env2/lib/python3.9/site-packages/sklearn/utils/_param_validation.py", line 95, in validate_parameter_constraints
#     raise InvalidParameterError(
# sklearn.utils._param_validation.InvalidParameterError: The 'zero_division' parameter of precision_score must be a float among {0.0, 1.0, nan} or a str among {'warn'}. Got nan instead.
...
[A bunch of these]
```

Labels: Bug