Typing: More precise NaT stub (#60002)

* more precise NaT stub

* ruff format

* updated == and != to return literal

pandas/_libs/tslibs/nattype.pyi

@@ -25,12 +25,8 @@ NaT: NaTType
 iNaT: int
 nat_strings: set[str]
 
-_NaTComparisonTypes: TypeAlias = (
-    datetime | timedelta | Period | np.datetime64 | np.timedelta64
-)
-
-class _NatComparison:
-    def __call__(self, other: _NaTComparisonTypes) -> bool: ...
+_TimeLike: TypeAlias = datetime | timedelta | Period | np.datetime64 | np.timedelta64
+_TimeDelta: TypeAlias = timedelta | np.timedelta64
 
 class NaTType:
     _value: np.int64
@@ -161,30 +157,30 @@ class NaTType:
     @property
     def qyear(self) -> float: ...
     # comparisons
-    def __eq__(self, other: object) -> bool: ...
-    def __ne__(self, other: object) -> bool: ...
-    __lt__: _NatComparison
-    __le__: _NatComparison
-    __gt__: _NatComparison
-    __ge__: _NatComparison
+    def __eq__(self, other: object, /) -> Literal[False]: ...
+    def __ne__(self, other: object, /) -> Literal[True]: ...
+    def __lt__(self, other: Self | _TimeLike, /) -> Literal[False]: ...
+    def __le__(self, other: Self | _TimeLike, /) -> Literal[False]: ...
+    def __gt__(self, other: Self | _TimeLike, /) -> Literal[False]: ...
+    def __ge__(self, other: Self | _TimeLike, /) -> Literal[False]: ...
     # unary operators
     def __pos__(self) -> Self: ...
     def __neg__(self) -> Self: ...
     # binary operators
-    def __sub__(self, other: Self | timedelta | datetime) -> Self: ...
-    def __rsub__(self, other: Self | timedelta | datetime) -> Self: ...
-    def __add__(self, other: Self | timedelta | datetime) -> Self: ...
-    def __radd__(self, other: Self | timedelta | datetime) -> Self: ...
-    def __mul__(self, other: float) -> Self: ...  # analogous to timedelta
-    def __rmul__(self, other: float) -> Self: ...
+    def __sub__(self, other: Self | _TimeLike, /) -> Self: ...
+    def __rsub__(self, other: Self | _TimeLike, /) -> Self: ...
+    def __add__(self, other: Self | _TimeLike, /) -> Self: ...
+    def __radd__(self, other: Self | _TimeLike, /) -> Self: ...
+    def __mul__(self, other: float, /) -> Self: ...  # analogous to timedelta
+    def __rmul__(self, other: float, /) -> Self: ...
     @overload  # analogous to timedelta
-    def __truediv__(self, other: Self | timedelta) -> float: ...  # Literal[NaN]
+    def __truediv__(self, other: Self | _TimeDelta, /) -> float: ...  # Literal[NaN]
     @overload
-    def __truediv__(self, other: float) -> Self: ...
+    def __truediv__(self, other: float, /) -> Self: ...
     @overload  # analogous to timedelta
-    def __floordiv__(self, other: Self | timedelta) -> float: ...  # Literal[NaN]
+    def __floordiv__(self, other: Self | _TimeDelta, /) -> float: ...  # Literal[NaN]
     @overload
-    def __floordiv__(self, other: float) -> Self: ...
+    def __floordiv__(self, other: float, /) -> Self: ...
     # other
     def __hash__(self) -> int: ...
     def as_unit(self, unit: str, round_ok: bool = ...) -> NaTType: ...