diff --git a/Misc/NEWS.d/next/Core and Builtins/2023-07-13-15-59-07.gh-issue-106719.jmVrsv.rst b/Misc/NEWS.d/next/Core and Builtins/2023-07-13-15-59-07.gh-issue-106719.jmVrsv.rst
new file mode 100644
index 00000000000..dc4bef193a3
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2023-07-13-15-59-07.gh-issue-106719.jmVrsv.rst	
@@ -0,0 +1,2 @@
+No longer suppress arbitrary errors in the ``__annotations__`` getter and
+setter in the type and module types.
diff --git a/Objects/moduleobject.c b/Objects/moduleobject.c
index 4071b5a3f1a..ba20534c3bd 100644
--- a/Objects/moduleobject.c
+++ b/Objects/moduleobject.c
@@ -937,26 +937,20 @@ static PyObject *
 module_get_annotations(PyModuleObject *m, void *Py_UNUSED(ignored))
 {
     PyObject *dict = PyObject_GetAttr((PyObject *)m, &_Py_ID(__dict__));
-
-    if ((dict == NULL) || !PyDict_Check(dict)) {
+    if (dict == NULL) {
+        return NULL;
+    }
+    if (!PyDict_Check(dict)) {
         PyErr_Format(PyExc_TypeError, "<module>.__dict__ is not a dictionary");
-        Py_XDECREF(dict);
+        Py_DECREF(dict);
         return NULL;
     }
 
-    PyObject *annotations;
-    /* there's no _PyDict_GetItemId without WithError, so let's LBYL. */
-    if (PyDict_Contains(dict, &_Py_ID(__annotations__))) {
-        annotations = PyDict_GetItemWithError(dict, &_Py_ID(__annotations__));
-        /*
-        ** _PyDict_GetItemIdWithError could still fail,
-        ** for instance with a well-timed Ctrl-C or a MemoryError.
-        ** so let's be totally safe.
-        */
-        if (annotations) {
-            Py_INCREF(annotations);
-        }
-    } else {
+    PyObject *annotations = PyDict_GetItemWithError(dict, &_Py_ID(__annotations__));
+    if (annotations) {
+        Py_INCREF(annotations);
+    }
+    else if (!PyErr_Occurred()) {
         annotations = PyDict_New();
         if (annotations) {
             int result = PyDict_SetItem(
@@ -975,8 +969,10 @@ module_set_annotations(PyModuleObject *m, PyObject *value, void *Py_UNUSED(ignor
 {
     int ret = -1;
     PyObject *dict = PyObject_GetAttr((PyObject *)m, &_Py_ID(__dict__));
-
-    if ((dict == NULL) || !PyDict_Check(dict)) {
+    if (dict == NULL) {
+        return -1;
+    }
+    if (!PyDict_Check(dict)) {
         PyErr_Format(PyExc_TypeError, "<module>.__dict__ is not a dictionary");
         goto exit;
     }
@@ -984,19 +980,17 @@ module_set_annotations(PyModuleObject *m, PyObject *value, void *Py_UNUSED(ignor
     if (value != NULL) {
         /* set */
         ret = PyDict_SetItem(dict, &_Py_ID(__annotations__), value);
-        goto exit;
     }
-
-    /* delete */
-    if (!PyDict_Contains(dict, &_Py_ID(__annotations__))) {
-        PyErr_Format(PyExc_AttributeError, "__annotations__");
-        goto exit;
+    else {
+        /* delete */
+        ret = PyDict_DelItem(dict, &_Py_ID(__annotations__));
+        if (ret < 0 && PyErr_ExceptionMatches(PyExc_KeyError)) {
+            PyErr_SetString(PyExc_AttributeError, "__annotations__");
+        }
     }
 
-    ret = PyDict_DelItem(dict, &_Py_ID(__annotations__));
-
 exit:
-    Py_XDECREF(dict);
+    Py_DECREF(dict);
     return ret;
 }
 
diff --git a/Objects/typeobject.c b/Objects/typeobject.c
index b1f9f1280fd..7e5282cabd1 100644
--- a/Objects/typeobject.c
+++ b/Objects/typeobject.c
@@ -1451,24 +1451,17 @@ type_get_annotations(PyTypeObject *type, void *context)
     }
 
     PyObject *annotations;
-    /* there's no _PyDict_GetItemId without WithError, so let's LBYL. */
     PyObject *dict = lookup_tp_dict(type);
-    if (PyDict_Contains(dict, &_Py_ID(__annotations__))) {
-        annotations = PyDict_GetItemWithError(dict, &_Py_ID(__annotations__));
-        /*
-        ** PyDict_GetItemWithError could still fail,
-        ** for instance with a well-timed Ctrl-C or a MemoryError.
-        ** so let's be totally safe.
-        */
-        if (annotations) {
-            if (Py_TYPE(annotations)->tp_descr_get) {
-                annotations = Py_TYPE(annotations)->tp_descr_get(
-                        annotations, NULL, (PyObject *)type);
-            } else {
-                Py_INCREF(annotations);
-            }
+    annotations = PyDict_GetItemWithError(dict, &_Py_ID(__annotations__));
+    if (annotations) {
+        if (Py_TYPE(annotations)->tp_descr_get) {
+            annotations = Py_TYPE(annotations)->tp_descr_get(
+                    annotations, NULL, (PyObject *)type);
+        } else {
+            Py_INCREF(annotations);
         }
-    } else {
+    }
+    else if (!PyErr_Occurred()) {
         annotations = PyDict_New();
         if (annotations) {
             int result = PyDict_SetItem(
@@ -1500,11 +1493,10 @@ type_set_annotations(PyTypeObject *type, PyObject *value, void *context)
         result = PyDict_SetItem(dict, &_Py_ID(__annotations__), value);
     } else {
         /* delete */
-        if (!PyDict_Contains(dict, &_Py_ID(__annotations__))) {
-            PyErr_Format(PyExc_AttributeError, "__annotations__");
-            return -1;
-        }
         result = PyDict_DelItem(dict, &_Py_ID(__annotations__));
+        if (result < 0 && PyErr_ExceptionMatches(PyExc_KeyError)) {
+            PyErr_SetString(PyExc_AttributeError, "__annotations__");
+        }
     }
 
     if (result == 0) {