sqlite3: handle return-type with factory argument. (#11571)

test_cases/stdlib/check_sqlite3.py

@@ -0,0 +1,26 @@
+from __future__ import annotations
+
+import sqlite3
+from typing_extensions import assert_type
+
+
+class MyConnection(sqlite3.Connection):
+    pass
+
+
+# Default return-type is Connection.
+assert_type(sqlite3.connect(":memory:"), sqlite3.Connection)
+
+# Providing an alternate factory changes the return-type.
+assert_type(sqlite3.connect(":memory:", factory=MyConnection), MyConnection)
+
+# Provides a true positive error. When checking the connect() function,
+# mypy should report an arg-type error for the factory argument.
+with sqlite3.connect(":memory:", factory=None) as con:  # type: ignore
+    pass
+
+# The Connection class also accepts a `factory` arg but it does not affect
+# the return-type. This use case is not idiomatic--connections should be
+# established using the `connect()` function, not directly (as shown here).
+assert_type(sqlite3.Connection(":memory:", factory=None), sqlite3.Connection)
+assert_type(sqlite3.Connection(":memory:", factory=MyConnection), sqlite3.Connection)