[python] Handle integer types more accurate in Python-to-C interface

[StrikerRUS]

The same as for R-package in #4291.

Match function signatures from https://github.com/microsoft/LightGBM/blob/master/include/LightGBM/c_api.h.

[jameslamb]

I went through this this morning. My review strategy was to pull up the Python package from this PR's branch and then the source of c_api.h in an editor, side-by-side.

I looked for each _LIB.something() call in the Python package and at the corresponding signature from the c_api header. All the signatures seem to match now, thanks very much!

[StrikerRUS]

@jameslamb Many thanks! My strategy was to search for ctypes. in basic.py file and track all calls of this module. I hope that two slightly different strategies give better chance to not overlook a mistake.

[github-actions]

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