[ENH] improved output type checking error messages in `BaseTransforme…

…r.transform` (#5921)

Improves output type checking error messages in
`BaseTransformer.transform`, using idiomatic `check_is_error_msg`.

Related: #5867

sktime/transformations/base.py

@@ -1227,20 +1227,32 @@ def _convert_output(self, X, metadata, inverse=False):
                 else:
                     Xt_metadata_required = []
 
-                valid, msg, metadata = check_is_mtype(
+                ALLOWED_OUT_MTYPES = ["pd.DataFrame", "pd.Series", "np.ndarray"]
+                Xt_valid, Xt_msg, metadata = check_is_mtype(
                     Xt,
-                    ["pd.DataFrame", "pd.Series", "np.ndarray"],
+                    ALLOWED_OUT_MTYPES,
                     msg_return_dict="list",
                     return_metadata=Xt_metadata_required,
                 )
 
-                if not valid:
-                    raise TypeError(
+                if not Xt_valid:
+                    Xtd = {k: v for k, v in Xt_msg.items() if k in ALLOWED_OUT_MTYPES}
+                    msg_start = (
+                        f"Type checking error in output of _transform of "
+                        f"{self.__class__.__name__}, output"
+                    )
+                    msg_out = (
                         f"_transform output of {type(self)} does not comply "
                         "with sktime mtype specifications. See datatypes.MTYPE_REGISTER"
-                        " for mtype specifications. Returned error message:"
-                        f" {msg}. Returned object: {Xt}"
+                        " for mtype specifications."
+                    )
+                    check_is_error_msg(
+                        Xtd,
+                        var_name=msg_start,
+                        allowed_msg=msg_out,
+                        raise_exception=True,
                     )
+
                 if X_input_mtype == "pd.Series" and not metadata["is_univariate"]:
                     X_output_mtype = "pd.DataFrame"
             elif self.get_tags()["scitype:transform-input"] == "Panel":