[4.1.x] Fixed #33919 -- Fixed adding AutoFields on PostgreSQL.

Thanks Jack Calvin Brown for the report.

Regression in 2eea361eff.
Backport of 5c803bc070 from main

django/db/backends/base/schema.py

@@ -637,6 +637,8 @@ class BaseDatabaseSchemaEditor:
         # It might not actually have a column behind it
         if definition is None:
             return
+        if col_type_suffix := field.db_type_suffix(connection=self.connection):
+            definition += f" {col_type_suffix}"
         # Check constraints can go on the column SQL here
         db_params = field.db_parameters(connection=self.connection)
         if db_params["check"]:

docs/releases/4.1.1.txt

@@ -35,3 +35,7 @@ Bugfixes
 
 * Fixed a bug in Django 4.1 that caused an incorrect validation of
   ``CheckConstraint()`` with range fields on PostgreSQL (:ticket:`33905`).
+
+* Fixed a regression in Django 4.1 that caused an incorrect migration when
+  adding ``AutoField``, ``BigAutoField``, or ``SmallAutoField`` on PostgreSQL
+  (:ticket:`33919`).

tests/schema/tests.py

@@ -792,6 +792,31 @@ class SchemaTests(TransactionTestCase):
         # Introspection treats BLOBs as TextFields
         self.assertEqual(columns["bits"][0], "TextField")
 
+    @isolate_apps("schema")
+    def test_add_auto_field(self):
+        class AddAutoFieldModel(Model):
+            name = CharField(max_length=255, primary_key=True)
+
+            class Meta:
+                app_label = "schema"
+
+        with connection.schema_editor() as editor:
+            editor.create_model(AddAutoFieldModel)
+        self.isolated_local_models = [AddAutoFieldModel]
+        old_field = AddAutoFieldModel._meta.get_field("name")
+        new_field = CharField(max_length=255)
+        new_field.set_attributes_from_name("name")
+        new_field.model = AddAutoFieldModel
+        with connection.schema_editor() as editor:
+            editor.alter_field(AddAutoFieldModel, old_field, new_field)
+        new_auto_field = AutoField(primary_key=True)
+        new_auto_field.set_attributes_from_name("id")
+        new_auto_field.model = AddAutoFieldModel()
+        with connection.schema_editor() as editor:
+            editor.add_field(AddAutoFieldModel, new_auto_field)
+        # Crashes on PostgreSQL when the GENERATED BY suffix is missing.
+        AddAutoFieldModel.objects.create(name="test")
+
     def test_remove_field(self):
         with connection.schema_editor() as editor:
             editor.create_model(Author)