`ValueError: Input contains NaN.` in `sklearn.manifold.smacof`

### Describe the bug

I accidentally stumbled onto a `ValueError` when executing `smacof`. I hacked into `_mds.py` to save both the offending `dissimilarities` as well as the randomly generated `X`, then cut them down to minimal shape that still exhibits the error. This data is attached below in the MCVE.

### Steps/Code to Reproduce

```
import numpy as np                          
import sklearn.manifold                     
                                            
dis = np.array([
    [0.0, 1.732050807568877, 1.7320508075688772], 
    [1.732050807568877, 0.0, 6.661338147750939e-16],
    [1.7320508075688772, 6.661338147750939e-16, 0.0]
])  
init = np.array([
    [0.08665881585055124, 0.7939114643387546],
    [0.9959834154297658, 0.7555546025640025],
    [0.8766008278401566, 0.4227358815811242]
])  
sklearn.manifold.smacof(dis, init=init, normalized_stress="auto", metric=False, n_init=1)
```

### Expected Results

No errors

### Actual Results

```
Traceback (most recent call last):
  File ".../rep_error.py", line 14, in <module>
    sklearn.manifold.smacof(dis, init=init, normalized_stress="auto", metric=False, n_init=1)
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/manifold/_mds.py", line 329, in smacof
    pos, stress, n_iter_ = _smacof_single(
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/manifold/_mds.py", line 128, in _smacof_single
    dis = euclidean_distances(X)
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/metrics/pairwise.py", line 310, in euclidean_distances
    X, Y = check_pairwise_arrays(X, Y)
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/metrics/pairwise.py", line 156, in check_pairwise_arrays
    X = Y = check_array(
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/utils/validation.py", line 959, in check_array
    _assert_all_finite(
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/utils/validation.py", line 124, in _assert_all_finite
    _assert_all_finite_element_wise(
  File ".../.direnv/python-3.9.5/lib/python3.9/site-packages/sklearn/utils/validation.py", line 173, in _assert_all_finite_element_wise
    raise ValueError(msg_err)
ValueError: Input contains NaN.
```

### Versions

```shell
System:
    python: 3.9.5 (default, Nov 23 2021, 15:27:38)  [GCC 9.3.0]
executable: .../.direnv/python-3.9.5/bin/python
   machine: Linux-5.4.0-148-generic-x86_64-with-glibc2.31

Python dependencies:
      sklearn: 1.3.0
          pip: 23.2.1
   setuptools: 44.0.0
        numpy: 1.25.1
        scipy: 1.11.1
       Cython: None
       pandas: None
   matplotlib: None
       joblib: 1.3.1
threadpoolctl: 3.2.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
    num_threads: 32
         prefix: libgomp
       filepath: .../.direnv/python-3.9.5/lib/python3.9/site-packages/scikit_learn.libs/libgomp-a34b3233.so.1.0.0
        version: None

       user_api: blas
   internal_api: openblas
    num_threads: 32
         prefix: libopenblas
       filepath: .../.direnv/python-3.9.5/lib/python3.9/site-packages/numpy.libs/libopenblas64_p-r0-7a851222.3.23.so
        version: 0.3.23
threading_layer: pthreads
   architecture: Zen

       user_api: blas
   internal_api: openblas
    num_threads: 32
         prefix: libopenblas
       filepath: .../.direnv/python-3.9.5/lib/python3.9/site-packages/scipy.libs/libopenblasp-r0-23e5df77.3.21.dev.so
        version: 0.3.21.dev
threading_layer: pthreads
   architecture: Zen
```

COMMENT:
@glemaitre Happy New Year! Gentle ping to look at my PR that should fix this and other related issues: https://github.com/scikit-learn/scikit-learn/pull/30514... It did not receive any feedback yet.

Labels: Bug, Needs Investigation