Intercepts of Newton-Cholesky logistic regression get corrupted when warm starting

### Describe the bug

When using multinomial logistic regression with warm starts from a previous iteration, the final coefficients in the model are correct, but the intercepts somehow get filled with incorrect numbers somewhere.

As a result, predictions from a warm-started model differ from those of a cold-start model that has more iterations on the same data.

The issue appears to have been introduced recently as it works fine with version 1.5, but not with 1.6 or 1.7.

### Steps/Code to Reproduce

```python
import numpy as np
from sklearn.datasets import load_iris
from sklearn.linear_model import LogisticRegression
X, y = load_iris(return_X_y=True)

model1 = LogisticRegression(
    solver="newton-cholesky",
    max_iter=2
).fit(X, y)
model2 = LogisticRegression(
    solver="newton-cholesky",
    max_iter=1,
    warm_start=True
).fit(X, y).fit(X, y)

np.testing.assert_almost_equal(
    model1.coef_,
    model2.coef_
)

np.testing.assert_almost_equal(
    model1.predict_proba(X[:5]),
    model2.predict_proba(X[:5])
)
```

### Expected Results

Intercepts should be the same, up to shifting by a constant if needed.

### Actual Results

Intercepts are different, as are predicted probabilities

### Versions

```shell
System:
    python: 3.12.6 | packaged by conda-forge | (main, Sep 22 2024, 14:16:49) [GCC 13.3.0]
executable: /home/david/miniforge3/bin/python
   machine: Linux-6.12.33+deb12-amd64-x86_64-with-glibc2.36

Python dependencies:
      sklearn: 1.7.1
          pip: 24.2
   setuptools: 74.1.2
        numpy: 2.0.1
        scipy: 1.14.1
       Cython: 3.1.0
       pandas: 2.2.3
   matplotlib: 3.9.2
       joblib: 1.4.2
threadpoolctl: 3.5.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
    num_threads: 20
         prefix: libscipy_openblas
       filepath: /home/david/.local/lib/python3.12/site-packages/numpy.libs/libscipy_openblas64_-99b71e71.so
        version: 0.3.27
threading_layer: pthreads
   architecture: Haswell

       user_api: blas
   internal_api: mkl
    num_threads: 14
         prefix: libmkl_rt
       filepath: /home/david/miniforge3/lib/libmkl_rt.so.2
        version: 2023.2-Product
threading_layer: gnu

       user_api: openmp
   internal_api: openmp
    num_threads: 20
         prefix: libgomp
       filepath: /home/david/miniforge3/lib/libgomp.so.1.0.0
        version: None
```

COMMENT:
In case it helps: it appears to be a matter of only one of the intercepts being off.

Example:
```python
import numpy as np
from sklearn.datasets import load_iris
from sklearn.linear_model import LogisticRegression
from scipy.special import softmax
X, y = load_iris(return_X_y=True)

model1 = LogisticRegression(
    solver="newton-cholesky",
    max_iter=2
).fit(X, y)
model2 = LogisticRegression(
    solver="newton-cholesky",
    max_iter=1,
    warm_start=True
).fit(X, y).fit(X, y)

np.testing.assert_almost_equal(
    model1.coef_,
    model2.coef_
)

np.testing.assert_almost_equal(
    softmax(
        model1.decision_function(X[:5])
    ),
    softmax(
        model2.decision_function(X[:5]) - np.array([0, 0, 3.16994517])
    )
)
```

Labels: Bug, module:linear_model