DOC: Ensure that we add documentation also as to the dict for types

This ensures that `help(np.dtype)` produces a result.  I am not
exactly sure why it picks up `__doc__` from the dict instead of
`tp_doc` right now. It probably is due to the combination of
inheritance and the fact that the dict always includes `None`
and gets preference during inheritance.
(That probably makes a lot of sense to not inherit the `type`
docstring by default.)

Modifying the dictionary directly is not really good style, either,
but hopefully works.

Closes numpygh-18740

numpy/core/src/multiarray/compiled_base.c

@@ -1425,9 +1425,23 @@ arr_add_docstring(PyObject *NPY_UNUSED(dummy), PyObject *args)
         PyCFunctionObject *new = (PyCFunctionObject *)obj;
         _ADDDOC(new->m_ml->ml_doc, new->m_ml->ml_name);
     }
-    else if (Py_TYPE(obj) == &PyType_Type) {
+    else if (PyObject_TypeCheck(obj, &PyType_Type)) {
+        /*
+         * We add it to both `tp_doc` and `__doc__` here.  Note that in theory
+         * `tp_doc` extracts the signature line, but we currently do not use
+         * it.  It may make sense to only add it as `__doc__` and
+         * `__text_signature__` to the dict in the future.
+         * The dictionary path is only necessary for heaptypes (currently not
+         * used) and metaclasses.
+         */
         PyTypeObject *new = (PyTypeObject *)obj;
         _ADDDOC(new->tp_doc, new->tp_name);
+        if (new->tp_dict != NULL && PyDict_CheckExact(new->tp_dict)) {
+            /* Warning: Modifying `tp_dict` is not generally safe! */
+            if (PyDict_SetItemString(new->tp_dict, "__doc__", str) < 0) {
+                return NULL;
+            }
+        }
     }
     else if (Py_TYPE(obj) == &PyMemberDescr_Type) {
         PyMemberDescrObject *new = (PyMemberDescrObject *)obj;