diff --git a/django/db/backends/mysql/features.py b/django/db/backends/mysql/features.py
index f2e4e1f1f4d..471853b1a3c 100644
--- a/django/db/backends/mysql/features.py
+++ b/django/db/backends/mysql/features.py
@@ -6,7 +6,7 @@ from django.utils.functional import cached_property
 
 class DatabaseFeatures(BaseDatabaseFeatures):
     empty_fetchmany_value = ()
-    allows_group_by_pk = True
+    allows_group_by_selected_pks = True
     related_fields_match_type = True
     # MySQL doesn't support sliced subqueries with IN/ALL/ANY/SOME.
     allow_sliced_subqueries_with_in = False
@@ -109,18 +109,6 @@ class DatabaseFeatures(BaseDatabaseFeatures):
                 "update.tests.AdvancedTests.test_update_ordered_by_m2m_annotation",
             },
         }
-        if "ONLY_FULL_GROUP_BY" in self.connection.sql_mode:
-            skips.update(
-                {
-                    "GROUP BY optimization does not work properly when "
-                    "ONLY_FULL_GROUP_BY mode is enabled on MySQL, see #31331.": {
-                        "aggregation.tests.AggregateTestCase."
-                        "test_aggregation_subquery_annotation_multivalued",
-                        "annotations.tests.NonAggregateAnnotationTestCase."
-                        "test_annotation_aggregate_with_m2o",
-                    },
-                }
-            )
         if self.connection.mysql_is_mariadb and (
             10,
             4,
diff --git a/django/db/models/sql/compiler.py b/django/db/models/sql/compiler.py
index f3b2b3da415..b6574eab2e9 100644
--- a/django/db/models/sql/compiler.py
+++ b/django/db/models/sql/compiler.py
@@ -235,7 +235,9 @@ class SQLCompiler:
             expressions = [
                 expr
                 for expr in expressions
-                if expr in pks or getattr(expr, "alias", None) not in aliases
+                if expr in pks
+                or expr in having
+                or getattr(expr, "alias", None) not in aliases
             ]
         return expressions