TYP: Narrow down type of method keyword in Index (pandas-dev#52723)

* Add literal type hint.

* Move type variable to _typing.py.

* Use existing type alias.

* EOF

Author: kklein

pandas/core/indexes/base.py

@@ -56,6 +56,7 @@
     JoinHow,
     Level,
     NaPosition,
+    ReindexMethod,
     Self,
     Shape,
     npt,
@@ -208,7 +209,6 @@
 _index_shared_docs: dict[str, str] = {}
 str_t = str
 
-
 _dtype_obj = np.dtype("object")
 
 _masked_engines = {
@@ -3755,7 +3755,7 @@ def get_loc(self, key):
     def get_indexer(
         self,
         target,
-        method: str_t | None = None,
+        method: ReindexMethod | None = None,
         limit: int | None = None,
         tolerance=None,
     ) -> npt.NDArray[np.intp]:
@@ -4208,7 +4208,7 @@ def _validate_can_reindex(self, indexer: np.ndarray) -> None:
     def reindex(
         self,
         target,
-        method=None,
+        method: ReindexMethod | None = None,
         level=None,
         limit: int | None = None,
         tolerance: float | None = None,