[C-API] Avoid C++ includes from arrow.h when including c_api.h

[desertstsung]

I've got the similar problem like #6839, while compling my C code. According to the issue, I found out that Ten0/lightgbm-rs@243322e is a good solution, but not so robust, so I made this fix.

[desertstsung]

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[jameslamb]

Thanks for your interest in LightGBM.

@Ten0 @borchero could you help review this?

[desertstsung]

Sorry for clicking Re-request review by accident.

[jameslamb]

/AzurePipelines run

[StrikerRUS]

/AzurePipelines run

[StrikerRUS]

/AzurePipelines run

[StrikerRUS]

/AzurePipelines run

[borchero]

I honestly don't know if this is the most ergonomic way to do this since I have too little experience with C(++) codebases 😅 as long as it works, I don't oppose it though