`type_of_target` returns 'multiclass' instead of 'continuous' on regression tasks with integer values e.g. house prices.

### Describe the bug

`utils.multiclass.type_of_target` returns 'multiclass' when y is the target of a regression problem that only takes integer values, even when cast to "float".

This appeared when I was working on the Ames housing dataset where prices are integers but represent a regression task. When splitting the dataset into train and test, the number of samples becomes less than half the number of 'classes' i.e. unique values so `type_of_target` raises the warning
"The number of unique classes is greater than 50% of the number "
"of samples. `y` could represent a regression problem, not a "
"classification problem."

This happened while using `RandomForestRegressor` with `oob_score=True` which calls `type_of_target(y)`. It can be fixed on the user side by adding some small non integer float to all elements of the target but I think this should be fixed on the library side. Note that casting the target type to "float" does not fix the issue.

### Steps/Code to Reproduce

```
from sklearn.datasets import fetch_openml
from sklearn.impute import SimpleImputer
from sklearn.model_selection import train_test_split
from sklearn.utils.multiclass import type_of_target

X, y = fetch_openml(data_id=42165, as_frame=True, return_X_y=True)
y = y.astype("float")

X = X.drop(columns="Id")
X = X.select_dtypes("number")

imputer = SimpleImputer(strategy="mean")
X = imputer.fit_transform(X)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

print(type_of_target(y_test))
```

### Expected Results

Outputs 'continuous' with no warning.

### Actual Results

```
typeoftarget_bug_reproducer.py:17: UserWarning: The number of unique classes is greater than 50% of the number of samples. `y` could represent a regression problem, not a classification problem.
  print(type_of_target(y_test))
multiclass
```
### Versions

```shell
System:
    python: 3.12.3 (main, Feb  4 2025, 14:48:35) [GCC 13.3.0]
executable: /home/gaeta/.sklearn-env/bin/python3
   machine: Linux-5.15.167.4-microsoft-standard-WSL2-x86_64-with-glibc2.39

Python dependencies:
      sklearn: 1.8.dev0
          pip: 25.1.1
   setuptools: 80.8.0
        numpy: 2.2.6
        scipy: 1.15.3
       Cython: 3.1.3
       pandas: 2.2.3
   matplotlib: 3.6.0
       joblib: 1.5.2
threadpoolctl: 3.6.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
    num_threads: 14
         prefix: libscipy_openblas
       filepath: /home/gaeta/.sklearn-env/lib/python3.12/site-packages/numpy.libs/libscipy_openblas64_-56d6093b.so
        version: 0.3.29
threading_layer: pthreads
   architecture: Haswell

       user_api: blas
   internal_api: openblas
    num_threads: 14
         prefix: libscipy_openblas
       filepath: /home/gaeta/.sklearn-env/lib/python3.12/site-packages/scipy.libs/libscipy_openblas-68440149.so
        version: 0.3.28
threading_layer: pthreads
   architecture: Haswell

       user_api: openmp
   internal_api: openmp
    num_threads: 14
         prefix: libgomp
       filepath: /usr/lib/x86_64-linux-gnu/libgomp.so.1.0.0
        version: None
```

COMMENT:
> I think the issue with TargetEncoder is a bit subtle, because it uses the keywords "multiclass"/"binary" and "continuous" to distinguish classification and regression while type_of_target uses the same keywords for something else. In the context of type_of_target, "multiclass" and "continuous" are not mutually exclusive.

I've looked into `TargetEncoder` and I agree with that `type_of_target` here is used in a different and maybe wrong way. Overall, `target_type="auto"` seems problematic.

If `TargetEncoder` with "auto" determines a target as "continuous" but the user wants to do a multiclass classification afterwards, then information is lost on squishing all the categories into mean values.

On the other hand, if it determines a target as "multiclass" but the user does a regression afterwards, the relation of the encoded features and the target is totally broken. At least I cannot see how columns with probabilities how the classes are represented in a continuous target would help a regression task.

Since we've seen several issues opened for this, I think it is better to not provide a default value for the `target_type` param, to force users to read the docs and detect our note (where we could also point out stronger that "auto" is to be used with caution). I'm happy to work on that. What do you think, @betatim @GaetandeCast @jeremiedbb?

Labels: Documentation