try fix typing

Author: jorisvandenbossche

pandas/_libs/index.pyi

@@ -54,7 +54,6 @@ class UInt16Engine(IndexEngine): ...
 class UInt8Engine(IndexEngine): ...
 class ObjectEngine(IndexEngine): ...
 class StringEngine(IndexEngine): ...
-class StringObjectEngine(ObjectEngine): ...
 class DatetimeEngine(Int64Engine): ...
 class TimedeltaEngine(DatetimeEngine): ...
 class PeriodEngine(Int64Engine): ...
@@ -73,6 +72,9 @@ class MaskedUInt16Engine(MaskedIndexEngine): ...
 class MaskedUInt8Engine(MaskedIndexEngine): ...
 class MaskedBoolEngine(MaskedUInt8Engine): ...
 
+class StringObjectEngine(ObjectEngine):
+    def __init__(self, values: object, na_value) -> None: ...
+
 class BaseMultiIndexCodesEngine:
     levels: list[np.ndarray]
     offsets: np.ndarray  # np.ndarray[..., ndim=1]

pandas/core/indexes/base.py

@@ -876,7 +876,7 @@ def _engine(
             # ndarray[Any, Any]]" has no attribute "_ndarray"  [union-attr]
             target_values = self._data._ndarray  # type: ignore[union-attr]
         elif is_string_dtype(self.dtype) and not is_object_dtype(self.dtype):
-            return libindex.StringObjectEngine(target_values, self.dtype.na_value)
+            return libindex.StringObjectEngine(target_values, self.dtype.na_value)  # type: ignore[union-attr]
 
         # error: Argument 1 to "ExtensionEngine" has incompatible type
         # "ndarray[Any, Any]"; expected "ExtensionArray"
@@ -6223,7 +6223,7 @@ def _maybe_downcast_for_indexing(self, other: Index) -> tuple[Index, Index]:
                 self = Index(self._values)
 
         elif self.dtype == "string" and other.dtype == "object":
-            if lib.is_string_array(other._values, skipna=True):
+            if lib.is_string_array(other._values, skipna=True):  # type: ignore[arg-type]
                 return self, other.astype(self.dtype)
 
         if not is_object_dtype(self.dtype) and is_object_dtype(other.dtype):