we don't do explicit fit_transform here, since it's a compound method.

Now I see:

From FeatureUnion's fit_transform we need to prepare for routing into three directions: to fit, to transform and to fit_transform. This is because of the way _fit_transform_one is designed:

        if hasattr(transformer, "fit_transform"):
            res = transformer.fit_transform(X, y, **params.get("fit_transform", {}))
        else:
            res = transformer.fit(X, y, **params.get("fit", {})).transform(
                X, **params.get("transform", {})
            )

It is designed this way, because a transformer can use either fit and transform or fit_transform and in fact, metadata routing is only possible, if it overwrites TransformerMixin's fit_transform.

But yes, we don't route from the FeaturUnion's fit to the estimator's fit_transform.

I've changed the routing to my new understandings.

We actually don't have a test for transformer.fit().transform(). I made one using a new class ConsumingNoFitTransformTransformer, that is special, because it doesn't inherit from TransformerMixin. it has a long name, but it's a speaking name. :)

We need this new class to make transformer.fit().transform() possible.

ConsumingClassifier's fit and transform would not be used, because it already has a fit_transform, that would be used instead.

I believe it needs to be like that:

                if hasattr(obj, "fit_transform"):
                    routed_params[name] = Bunch(fit_transform={})
                    routed_params[name].fit_transform = params
                else:
                    routed_params[name] = Bunch(fit={})
                    routed_params[name] = Bunch(transform={})
                    routed_params[name].fit = params
                    routed_params[name].transform = params

It accounts for the metadata to be passed to the correct methods of the sub-transformer. I've also added a test for that (test_feature_union_fit_params_without_fit_transform).