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:
> could you explain this a bit more? I was thinking about things like `RandomSearchCV` as a way to train models and "using" the results of the metric. But I think for the random search use-case it doesn't matter what namespace the metric is in.
> 

So basically if you train models using HuggingFace and you want to compute metrics you need to move the arrays to cpu and convert to numpy before this can be done. Here is the code from the generic trainer class that does this /https://github.com/huggingface/transformers/blob/main/src/transformers/trainer.py#L4420-L4439

Labels: Needs Decision, Array API