BUG loss of precision in LogisticRegression as of version 1.4

### Describe the bug

Between version 1.3.2 and 1.4.0, LogisticRegression became less accurate.

### Steps/Code to Reproduce

```python
import numpy as np
import pandas as pd

import sklearn.pipeline
import sklearn.preprocessing
import sklearn.linear_model

df = pd.DataFrame({
    'age': [0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],
    'exiting':  [False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]
})

data_timeline = np.arange(df['age'].max() + 1)

estimator = sklearn.pipeline.Pipeline(
    [
        (
            "onehot",
            sklearn.preprocessing.OneHotEncoder(
                categories=[data_timeline], sparse_output=False
            )
        ),
        (
            "logistic",
            sklearn.linear_model.LogisticRegression(
                fit_intercept=False, C=1e6, max_iter=1000, tol=1e-7, solver="newton-cg"
            ),
        ),
    ]
)

estimator.fit(df[['age']], df["exiting"])
def logistic_regression_gradient(X, y, y_hat, coef, C):
    return coef + C * (y_hat - y) @ X

gradient = logistic_regression_gradient(
    X=estimator.named_steps['onehot'].transform(df[['age']]),
    y=df["exiting"].astype(float).to_numpy(),
    y_hat=estimator.predict_proba(df[['age']])[:, 1],
    coef=estimator.named_steps["logistic"].coef_,
    C=estimator.named_steps['logistic'].C
)
print(sklearn.__version__)
print(gradient)
```

### Expected Results

```
1.3.2
[[ 6.38057971e-06 -1.47032373e-02  3.23092176e-06 -1.86882858e-02
  -1.85588401e-02 -7.10504243e-05  8.47822321e-05 -1.58804369e-02
  -1.58804369e-02 -1.58804369e-02 -1.58804369e-02 -1.18021221e-02
  -2.76625890e-03 -2.76625890e-03 -2.76625890e-03 -2.76625890e-03
  -2.76625890e-03 -2.76625890e-03 -2.76625890e-03  0.00000000e+00
   2.22974349e-02  2.22974349e-02  2.22974349e-02  2.22974349e-02
   2.22974349e-02  2.22974349e-02  2.22974349e-02  2.22974349e-02
   2.22974349e-02  2.22974349e-02  2.22974349e-02  2.22974349e-02
   2.22974349e-02]]
```

### Actual Results

```
1.4.0
[[ 2.68892818e-03  3.64025037e+00  6.76589138e-04  3.77020823e+00
   3.80372303e+00 -1.41805879e-04  1.51207953e-02  3.89408378e+00
   3.89408378e+00  3.89408378e+00  3.89408378e+00  3.96014198e+00
   4.05600402e+00  4.05600402e+00  4.05600402e+00  4.05600402e+00
   4.05600402e+00  4.05600402e+00  4.05600402e+00  0.00000000e+00
   4.22741992e+00  4.22741992e+00  4.22741992e+00  4.22741992e+00
   4.22741992e+00  4.22741992e+00  4.22741992e+00  4.22741992e+00
   4.22741992e+00  4.22741992e+00  4.22741992e+00  4.22741992e+00
   4.22741992e+00]]
```

### Versions

```shell
System:
    python: 3.12.2 | packaged by conda-forge | (main, Feb 16 2024, 20:50:58) [GCC 12.3.0]
executable: ~/miniforge3/envs/sklearn-env/bin/python
   machine: Linux-6.8.1-arch1-1-x86_64-with-glibc2.39

Python dependencies:
      sklearn: 1.4.0
          pip: 24.0
   setuptools: 69.2.0
        numpy: 1.26.4
        scipy: 1.12.0
       Cython: 3.0.9
       pandas: 2.2.1
   matplotlib: None
       joblib: 1.3.2
threadpoolctl: 3.4.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
    num_threads: 8
         prefix: libopenblas
       filepath: ~/miniforge3/envs/sklearn-env/lib/libopenblasp-r0.3.26.so
        version: 0.3.26
threading_layer: pthreads
   architecture: Zen

       user_api: openmp
   internal_api: openmp
    num_threads: 8
         prefix: libgomp
       filepath: ~/miniforge3/envs/sklearn-env/lib/libgomp.so.1.0.0
        version: None
```
```

COMMENT:
We do not expose the gradient publicly. Maybe, we should change the use guide in https://scikit-learn.org/stable/modules/linear_model.html#binary-case. Liblinear is the only solver with that exact objective, all others are more consistent with the GLM formulation, Ridge and Lasso included.

Labels: Bug, module:linear_model, Numerical Stability