[python-package] fix mypy errors for eval_at and basic

[IdoKendo]

Contributes to #3867.
Moved from #5672.

Fixes mypy errors regarding eval_at incompatibility:

Argument "eval_at" to "_train" has incompatible type "Optional[Iterable[int]]"; expected "Union[List[int], Tuple[int], None]"  [arg-type]

and the following two errors:

python-package\lightgbm\engine.py:169: error: Argument 1 to "set_feature_name" of "Dataset" has incompatible type "Union[List[str], str]"; expected "List[str]"  [arg-type]
python-package\lightgbm\engine.py:170: error: Argument 1 to "set_categorical_feature" of "Dataset" has incompatible type "Union[List[str], List[int], str]"; expected "Union[List[int], List[str]]"  [arg-type]

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]

Thanks again for working on this! I left one question for your consideration.

[jameslamb]

Why is Union[something, something_else, None] preferable to Optional[Union[something, something_else]]? If that's just a personal style preference thing, please revert that part of this change. I personally prefer the Optional[] form.

[IdoKendo]

Yeah, no problem, changed it to Optional[] form.

[jameslamb]

Thanks so much, changes look great to me! I just merged latest master into this, will merge this once CI passes.

[github-actions]

This pull request has been automatically locked since there has not been any recent activity since it was closed.
To start a new related discussion, open a new issue at https://github.com/microsoft/LightGBM/issues
including a reference to this.