Clarification of output array type when metrics accept multiclass/multioutput

Clarification of how we should handle array output type when a metric outputs several values (i.e. accepts multiclass or multioutput input).

The issue was summarised succinctly in https://github.com/scikit-learn/scikit-learn/pull/30439#issuecomment-2532238196:

> Not sure what should be the output namespace / device in case we output an array, e.g. roc_auc_score with average=None on multiclass problems...

Currently all regression/classification metrics that support array API and multiclass or multioutput, all output an array in the same namespace and device as the input (checked code and manually). Summary of these metrics :

### Regression metrics

Returns array in same namespace/device:
* [explained_variance_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.explained_variance_score.html#sklearn.metrics.explained_variance_score)
* [r2_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score) 
* [mean_absolute_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_absolute_error.html#sklearn.metrics.mean_absolute_error)
* [mean_absolute_percentage_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_absolute_percentage_error.html#sklearn.metrics.mean_absolute_percentage_error)
* [mean_pinball_loss](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_pinball_loss.html#sklearn.metrics.mean_pinball_loss)
* [mean_squared_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_squared_error.html#sklearn.metrics.mean_squared_error)
* [mean_squared_log_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_squared_log_error.html#sklearn.metrics.mean_squared_log_error)
* [root_mean_squared_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.root_mean_squared_error.html#sklearn.metrics.root_mean_squared_error)
* [root_mean_squared_log_error](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.root_mean_squared_log_error.html#sklearn.metrics.root_mean_squared_log_error)

### Classification metrics
Returns array in same namespace/device:

* [precision_recall_fscore_support](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.precision_recall_fscore_support.html#sklearn.metrics.precision_recall_fscore_support) and family ([f1_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score), [fbeta_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.fbeta_score.html#sklearn.metrics.fbeta_score), [precision_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.precision_score.html#sklearn.metrics.precision_score), [recall_score](https://scikit-learn.org/dev/modules/generated/sklearn.metrics.recall_score.html#sklearn.metrics.recall_score))

Looking at the metrics code, if we wanted to support a list of scalars, we'd generally have to do extra processing to convert an array (often output of an xp.** function) to a list of scalars.

Once we arrive at a consensus we should update the array API documentation and update the `check_array_api_metric` in tests such that when the output is array/list - we check that the output type etc is correct.

cc @ogrisel @betatim

COMMENT:
Reading through this thread, here's what I see:

- we don't have a real common usecase in mind where the output staying in the original space makes users' life easier
- we have cases where returning numpy as we do now, makes users' lives easier in some cases in existing common usecases

Also:
- we return numpy arrays now, so keeping the current behavior means users not having to change anything in their code
- when scorers return single values, it's a python float, not even a numpy float, so our scorer outputs are not in the same "kind" as the input anyway


So in the end, it seams what returning the result in the same space as the input brings, is to make us happy that we're "consistent" in some way, but it doesn't seem to bring much of a value to the user. On the other hand, returning numpy arrays is a much "simpler" kind of output which to me seems closer to the idea of returning python floats on single values.

That to me indicates returning numpy arrays is winning the argument here.

Labels: Needs Decision, Array API