Handle Annotated types in _serialize_python_type for TypedDict generation

src/datamodel_code_generator/__main__.py

@@ -856,7 +856,7 @@ def _get_preserved_type_origins() -> dict[type, str]:
     return _PRESERVED_TYPE_ORIGINS
 
 
-def _serialize_python_type(tp: type) -> str | None:
+def _serialize_python_type(tp: type) -> str | None:  # noqa: PLR0911
     """Serialize Python type to a string for x-python-type field.
 
     Returns None if the type doesn't need to be preserved (e.g., standard dict, list).
@@ -884,6 +884,14 @@ def _serialize_python_type(tp: type) -> str | None:
                 return " | ".join(n or _simple_type_name(a) for n, a in zip(nested, args, strict=False))
         return None  # pragma: no cover
 
+    # Handle Annotated types - extract the base type and ignore metadata
+    from typing import Annotated  # noqa: PLC0415
+
+    if origin is Annotated:
+        if args:
+            return _serialize_python_type(args[0]) or _simple_type_name(args[0])
+        return None  # pragma: no cover
+
     type_name: str | None = None
     if origin is not None:
         type_name = preserved_origins.get(origin)