[python-package] Fix mypy errors for predict() method

[IdoKendo]

Contributes to #3867.
Moved from #5672.
mypy currently raises the following errors regarding predict() method:

python-package\lightgbm\dask.py:1224: error: Signature of "predict" incompatible with supertype "LGBMClassifier"  [override]
python-package\lightgbm\dask.py:1224: note:      Superclass:
python-package\lightgbm\dask.py:1224: note:          def predict(self, X: Any, raw_score: bool = ..., start_iteration: int = ..., num_iteration: Optional[int] = ..., pred_leaf: bool = ..., pred_contrib: bool = ..., validate_features: bool = ..., **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1224: note:      Subclass:
python-package\lightgbm\dask.py:1224: note:          def predict(self, X: Union[Any, Any], **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1224: error: Signature of "predict" incompatible with supertype "LGBMModel"  [override]
python-package\lightgbm\dask.py:1224: note:          def predict(self, X: Any, raw_score: bool = ..., start_iteration: int = ..., num_iteration: Optional[int] = ..., pred_leaf: bool = ..., pred_contrib: bool = ..., validate_features: bool = ..., **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1224: note:          def predict(self, X: Union[Any, Any], **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1397: error: Signature of "predict" incompatible with supertype "LGBMModel"  [override]
python-package\lightgbm\dask.py:1397: note:      Superclass:
python-package\lightgbm\dask.py:1397: note:          def predict(self, X: Any, raw_score: bool = ..., start_iteration: int = ..., num_iteration: Optional[int] = ..., pred_leaf: bool = ..., pred_contrib: bool = ..., validate_features: bool = ..., **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1397: note:      Subclass:
python-package\lightgbm\dask.py:1397: note:          def predict(self, X: Union[Any, Any], **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1555: error: Signature of "predict" incompatible with supertype "LGBMModel"  [override]
python-package\lightgbm\dask.py:1555: note:      Superclass:
python-package\lightgbm\dask.py:1555: note:          def predict(self, X: Any, raw_score: bool = ..., start_iteration: int = ..., num_iteration: Optional[int] = ..., pred_leaf: bool = ..., pred_contrib: bool = ..., validate_features: bool = ..., **kwargs: Any) -> Any
python-package\lightgbm\dask.py:1555: note:      Subclass:
python-package\lightgbm\dask.py:1555: note:          def predict(self, X: Union[Any, Any], **kwargs: Any) -> Any

Notes for Reviewers

This was tested by running mypy as documented in #3867.

mypy \
    --exclude='python-package/compile/|python-package/build' \
    --ignore-missing-imports \
    python-package/

[jameslamb]

Very nice, thanks!

I think the slight added maintenance burden of keeping this in sync with the interface in lightgbm.sklearn is worth it in exchange for mypy being better-able to walk through the Dask*.predict() methods' code (which wouldn't be the case if we instead resolved these particular warnings with # type: ignore comments).

And once mypy checks are fully enabled and cause CI failures, that tool will even alert on issues of the form "hey you changed the lightgbm.sklearn.LGBMClassifier.predict() signature but didn't make the same changes on the Dask side".

[github-actions]

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