Cloned estimators have identical randomness but different RNG instances

### Describe the bug

Cloned estimators have identical randomness but different RNG instances. According to documentation, it should be the other way around: different randomness but identical RNG instances.

Related #25395 

The User Guide [says](https://scikit-learn.org/stable/common_pitfalls.html#controlling-randomness):
> For an optimal robustness of cross-validation (CV) results, pass RandomState instances when creating estimators

> ```python
> rf_inst = RandomForestClassifier(random_state=np.random.RandomState(0))
> cross_val_score(rf_inst, X, y)
> ```
> ...
> Since `rf_inst` was passed a `RandomState` instance, each call to `fit` starts from a different RNG. As a result, the random subset of features will be different for each folds

In regards to cloning, the same reference says:
> ```python
> rng = np.random.RandomState(0)
> a = RandomForestClassifier(random_state=rng)
> b = clone(a)
> ```
> Moreover, `a` and `b` will influence each-other since they share the same internal RNG: calling `a.fit` will consume `b`’s RNG, and calling `b.fit` will consume `a`’s RNG, since they are the same. 

The actual behaviour does not follow this description. 

### Steps/Code to Reproduce

```python
import numpy as np
from sklearn import clone
from sklearn.datasets import make_classification
from sklearn.model_selection import cross_validate
from sklearn.ensemble import RandomForestClassifier

rng = np.random.RandomState(0)
X, y = make_classification(random_state=rng)
rf = RandomForestClassifier(random_state=rng)

d = cross_validate(rf, X, y, return_estimator=True, cv=2)
rngs = [e.random_state for e in d['estimator']]
# estimators corresponding to different CV runs have different but identical RNGs:
print(rngs[0] is rngs[1]) # False
print(all(rngs[0].randint(10, size=10) == rngs[1].randint(10, size=10))) # True

rf_clone = clone(rf)
rngs = [rf.random_state, rf_clone.random_state]
print(rngs[0] is rngs[1]) # False
print(all(rngs[0].randint(10, size=10) == rngs[1].randint(10, size=10))) # True
```

### Expected Results

True False True False

### Actual Results

False True False True

### Versions

```shell
Tested on a two-week-old dev build and also on the following version (Kaggle)

System:
    python: 3.7.12 | packaged by conda-forge | (default, Oct 26 2021, 06:08:53)  [GCC 9.4.0]
executable: /opt/conda/bin/python3.7
   machine: Linux-5.15.90+-x86_64-with-debian-bullseye-sid

Python dependencies:
          pip: 22.3.1
   setuptools: 59.8.0
      sklearn: 1.0.2
        numpy: 1.21.6
        scipy: 1.7.3
       Cython: 0.29.34
       pandas: 1.3.5
   matplotlib: 3.5.3
       joblib: 1.2.0
threadpoolctl: 3.1.0

Built with OpenMP: True
```

COMMENT:
I think it is worth slowing down, because it is a hairy issue and the impact is also big. The good thing is that its probably been the way it is now for a while, so spending an extra moment to disentangle things is not a big cost.

I also thought that what the docs describe is how it should be as well as how it is.

However, Nicolas' code fails for me on version 1.0.2 (same with the SGD based example). This is doubly weird because the docstring of `clone` explicitly talks about how `random_state` is handled in a special way.

Labels: Bug, Documentation, Needs Decision