Fix caster optimization regression introduced in #3650 (#3659)

* Fix optimization bug introduced in #3650

* Add simple Python extension test for MVF

* Improve comments

* Clarify comment

* Clarify another comment

* Add test docstring

* Fix typo

include/pybind11/detail/internals.h

@@ -200,7 +200,9 @@ struct type_info {
     void *get_buffer_data = nullptr;
     void *(*module_local_load)(PyObject *, const type_info *) = nullptr;
     /* A simple type never occurs as a (direct or indirect) parent
-     * of a class that makes use of multiple inheritance */
+     * of a class that makes use of multiple inheritance.
+     * A type can be simple even if it has non-simple ancestors as long as it has no descendants.
+     */
     bool simple_type : 1;
     /* True if there is no multiple inheritance in this type's inheritance tree */
     bool simple_ancestors : 1;

include/pybind11/pybind11.h

@@ -1206,13 +1206,14 @@ protected:
         if (rec.bases.size() > 1 || rec.multiple_inheritance) {
             mark_parents_nonsimple(tinfo->type);
             tinfo->simple_ancestors = false;
-            tinfo->simple_type = false;
         }
         else if (rec.bases.size() == 1) {
-            auto parent_tinfo = get_type_info((PyTypeObject *) rec.bases[0].ptr());
-            tinfo->simple_ancestors = parent_tinfo->simple_ancestors;
-            // a child of a non-simple type can never be a simple type
-            tinfo->simple_type = parent_tinfo->simple_type;
+            auto *parent_tinfo = get_type_info((PyTypeObject *) rec.bases[0].ptr());
+            assert(parent_tinfo != nullptr);
+            bool parent_simple_ancestors = parent_tinfo->simple_ancestors;
+            tinfo->simple_ancestors = parent_simple_ancestors;
+            // The parent can no longer be a simple type if it has MI and has a child
+            parent_tinfo->simple_type = parent_tinfo->simple_type && parent_simple_ancestors;
         }
 
         if (rec.module_local) {

tests/test_multiple_inheritance.cpp

@@ -235,7 +235,7 @@ TEST_SUBMODULE(multiple_inheritance, m) {
     // - functions are get_{base}_{var}, return {var}
     struct MVB {
         MVB() = default;
-        MVB(const MVB&) = default;
+        MVB(const MVB &) = default;
         virtual ~MVB() = default;
 
         int b = 1;

tests/test_multiple_inheritance.py

@@ -472,3 +472,25 @@ def test_pr3635_diamond_f():
     assert o.get_f_e() == 5
 
     assert o.get_f_f() == 6
+
+
+def test_python_inherit_from_mi():
+    """Tests extending a Python class from a single inheritor of a MI class"""
+
+    class PyMVF(m.MVF):
+        g = 7
+
+        def get_g_g(self):
+            return self.g
+
+    o = PyMVF()
+
+    assert o.b == 1
+    assert o.c == 2
+    assert o.d0 == 3
+    assert o.d1 == 4
+    assert o.e == 5
+    assert o.f == 6
+    assert o.g == 7
+
+    assert o.get_g_g() == 7