Fix `typing.TypeAliasType` being undefined on python < 3.12 (#17558)

Closes #17554
CC @JukkaL 
Refs https://github.com/python/mypy/pull/17320

mypy/checkexpr.py

diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index ad1b416..9dee743 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -4679,7 +4679,7 @@
         """
         if isinstance(tapp.expr, RefExpr) and isinstance(tapp.expr.node, TypeAlias):
             if tapp.expr.node.python_3_12_type_alias:
-                return self.named_type("typing.TypeAliasType")
+                return self.type_alias_type_type()
             # Subscription of a (generic) alias in runtime context, expand the alias.
             item = instantiate_type_alias(
                 tapp.expr.node,
@@ -4743,7 +4743,7 @@
             y = cast(A, ...)
         """
         if alias.python_3_12_type_alias:
-            return self.named_type("typing.TypeAliasType")
+            return self.type_alias_type_type()
         if isinstance(alias.target, Instance) and alias.target.invalid:  # type: ignore[misc]
             # An invalid alias, error already has been reported
             return AnyType(TypeOfAny.from_error)
@@ -5863,6 +5863,12 @@
         """
         return self.chk.named_type(name)
 
+    def type_alias_type_type(self) -> Instance:
+        """Returns a `typing.TypeAliasType` or `typing_extensions.TypeAliasType`."""
+        if self.chk.options.python_version >= (3, 12):
+            return self.named_type("typing.TypeAliasType")
+        return self.named_type("typing_extensions.TypeAliasType")
+
     def is_valid_var_arg(self, typ: Type) -> bool:
         """Is a type valid as a *args argument?"""
         typ = get_proper_type(typ)

test-data/unit/check-type-aliases.test

diff --git a/test-data/unit/check-type-aliases.test b/test-data/unit/check-type-aliases.test
index 6f9e9ed..c7b9694 100644
--- a/test-data/unit/check-type-aliases.test
+++ b/test-data/unit/check-type-aliases.test
@@ -1074,7 +1074,7 @@
 y: TestType = 'a'
 z: TestType = object()  # E: Incompatible types in assignment (expression has type "object", variable has type "Union[int, str]")
 
-reveal_type(TestType)  # N: Revealed type is "typing.TypeAliasType"
+reveal_type(TestType)  # N: Revealed type is "typing_extensions.TypeAliasType"
 TestType()  # E: "TypeAliasType" not callable
 
 class A:
@@ -1084,6 +1084,15 @@
 [builtins fixtures/tuple.pyi]
 [typing fixtures/typing-full.pyi]
 
+[case testTypeAliasTypePython311]
+# flags: --python-version 3.11
+# Pinning to 3.11, because 3.12 has `TypeAliasType`
+from typing_extensions import TypeAliasType
+
+TestType = TypeAliasType("TestType", int)
+x: TestType = 1
+[builtins fixtures/tuple.pyi]
+
 [case testTypeAliasTypeInvalid]
 from typing_extensions import TypeAliasType