GridSearchCV.verbose documentation does not match actual behavior (values >3, >10)

### Describe the issue linked to the documentation

[`GridSearchCV` docs ](https://scikit-learn.org/1.7/modules/generated/sklearn.model_selection.GridSearchCV.html) state

> **verbose** int
> Controls the verbosity: the higher, the more messages.
> \>1 : the computation time for each fold and parameter candidate is displayed;
> \>2 : the score is also displayed;
> \>3 : the fold and candidate parameter indexes are also displayed together with the starting time of the computation.

In reality, this param is passed to joblib [here](https://github.com/scikit-learn/scikit-learn/blob/d3898d9d57aeb1e960d266613a2e31b07bca39d7/sklearn/model_selection/_search.py#L1009), whose [docs](https://joblib.readthedocs.io/en/latest/generated/joblib.Parallel.html) state:
> **verbose**: int, default=0
> The verbosity level: if non zero, progress messages are printed. Above 50, the output is sent to stdout. The frequency of the messages increases with the verbosity level. If it more than 10, all iterations are reported.

Testing with the MRE below shows that 0 is silent, 1 prints one line, 2 prints a line for each CV split. 3-9 are all the same. 10-inf are all the same

### MRE:
```python
from sklearn.model_selection import GridSearchCV
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import make_classification

X, y = make_classification()

clf = LogisticRegression(max_iter=100)

param_grid = {"C": [1, 2]}

for v in [0, 1, 2, 3, 9, 10, 1000]:
    print(f"\n=======  verbose={v}  ======= ")
    gs = GridSearchCV(
        clf,
        param_grid,
        cv=2,
        n_jobs=1,
        verbose=v,
    )
    gs.fit(X, y)
```

It is possible taht the same issue exists elsewhere, I've not looked thoroughly

### Suggest a potential alternative/fix

Update docs to match observed behaviour, e.g.:

> **verbose** int
> Controls the verbosity: the higher, the more messages.
> 0 : no messages;
> 1 : a single line describing the number of folds, the number of candidates, and the number of fits;
> 2 : the above, plus when each fold ends, the computation time for that fold and parameter candidate is displayed;
> 3-9 : the above, plus the fold index and the score is also displayed;
> ≥10 : an additional message for the start of each fold, and the candidate parameter indexes are also displayed.

COMMENT:
Thanks @StefanieSenger 

> The CV folds are in the outer loop  

Good point - I'd not actually thought carefully about the order of the loops. From the output when `verbose=10` I'd understood it looped over each param candidate and then over the splits - as it shows CVs 1&2 for candidate 1 (`C=1`), and only then CVs 1&2 for candidate 2 (`C=2`) - am I mistaken? This seems to be the relevant bit of [code](https://github.com/scikit-learn/scikit-learn/blob/04c9f3eee9dafa76b92bc589e55e700398ca6e10/sklearn/model_selection/_search.py#L999C1-L1016C1)  
```python
                    for (cand_idx, parameters), (split_idx, (train, test)) in product(
                        enumerate(candidate_params),
                        enumerate(cv.split(X, y, **routed_params.splitter.split)),
                    )
```
if I understand [itertools.product](https://docs.python.org/3/library/itertools.html#itertools.product) correctly, isn't the first arg used as the outer loop? Apologies if I'm misunderstanding

> if we keep the verbosity logging-like (which we do want), so it gets displayed real time to track progress  

fully agree, verbose output def needs to be in real time.  

OK let's leave it as a docs change for now as you suggest 😃

Labels: Documentation