TYP: Add typing.overload signatures to DataFrame/Series.interpolate (#…

…54999)

* Add inplace overloads for  interpolate

This will help our type checker work better and is a plain improvement to the type hints.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

pandas/core/generic.py

@@ -7938,6 +7938,51 @@ def replace(
         else:
             return result.__finalize__(self, method="replace")
 
+    @overload
+    def interpolate(
+        self,
+        method: InterpolateOptions = ...,
+        *,
+        axis: Axis = ...,
+        limit: int | None = ...,
+        inplace: Literal[False] = ...,
+        limit_direction: Literal["forward", "backward", "both"] | None = ...,
+        limit_area: Literal["inside", "outside"] | None = ...,
+        downcast: Literal["infer"] | None | lib.NoDefault = ...,
+        **kwargs,
+    ) -> Self:
+        ...
+
+    @overload
+    def interpolate(
+        self,
+        method: InterpolateOptions = ...,
+        *,
+        axis: Axis = ...,
+        limit: int | None = ...,
+        inplace: Literal[True],
+        limit_direction: Literal["forward", "backward", "both"] | None = ...,
+        limit_area: Literal["inside", "outside"] | None = ...,
+        downcast: Literal["infer"] | None | lib.NoDefault = ...,
+        **kwargs,
+    ) -> None:
+        ...
+
+    @overload
+    def interpolate(
+        self,
+        method: InterpolateOptions = ...,
+        *,
+        axis: Axis = ...,
+        limit: int | None = ...,
+        inplace: bool_t = ...,
+        limit_direction: Literal["forward", "backward", "both"] | None = ...,
+        limit_area: Literal["inside", "outside"] | None = ...,
+        downcast: Literal["infer"] | None | lib.NoDefault = ...,
+        **kwargs,
+    ) -> Self | None:
+        ...
+
     @final
     def interpolate(
         self,