[python-package] fix mypy errors about callbacks

[jameslamb]

Contributes to #3756.
Contributes to #3867.

mypy currently raises the following errors.

-python-package/lightgbm/engine.py:688: error: Incompatible types in assignment (expression has type "Set[<nothing>]", variable has type "Optional[List[Callable[..., Any]]]")
-python-package/lightgbm/engine.py:692: error: Incompatible types in assignment (expression has type "Set[Callable[..., Any]]", variable has type "Optional[List[Callable[..., Any]]]")
-python-package/lightgbm/engine.py:695: error: Item "List[Callable[..., Any]]" of "Optional[List[Callable[..., Any]]]" has no attribute "add"
-python-package/lightgbm/engine.py:695: error: Item "None" of "Optional[List[Callable[..., Any]]]" has no attribute "add"
-python-package/lightgbm/engine.py:707: error: Item "None" of "Optional[List[Callable[..., Any]]]" has no attribute "__iter__" (not iterable)
-python-package/lightgbm/engine.py:708: error: Unsupported left operand type for - ("List[Callable[..., Any]]")
-python-package/lightgbm/engine.py:708: error: Unsupported left operand type for - ("None")
-python-package/lightgbm/engine.py:708: note: Left operand is of type "Optional[List[Callable[..., Any]]]"
-python-package/lightgbm/engine.py:709: error: Incompatible types in assignment (expression has type "List[Union[Callable[..., Any], Any]]", variable has type "Set[Union[Callable[..., Any], Any]]")

These errors come from variables' types changing. Specifically, the fact that in the code for cv(), the variable callbacks is initially assigned a value with type Optional[List[Callable]], then is overwritten with a set, then the variable callbacks_before_iter is initialized as a set and overwritten with a list.

Similar to #5447, this PR proposes fixing those errors by using differently-named variables when types change.

Notes for Reviewers

The same changes proposed in this PR were implemented in #4839 to fix the same code in train().

I tested this by running mypy as documented in #3867.

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

[StrikerRUS]

Thanks for fixing this!

[github-actions]

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