Use modern C++ casts instead of current C-style casting approaches

### Description

Update various API implementations that use c-style pointer casting and other c-style approaches to use modern C++ casts.

### Is this a breaking change?

The function signatures would remain unchanged
The behavior of the functions would be identical
User code that calls these functions wouldn't need any modifications

### Additional information

Modernizes the code base. Compilers will optimize these the same, but coding standards favor using C++ cast in C++ code.

まず、C-style pointer casts またはその他の C-style casting approaches を使用している API 実装を見つけます。関連する casts を modern C++ casts に置き換え、function signatures と動作を維持したうえで、実装が引き続きビルドでき、同一の動作をすることを確認します。

索引モデルが issue の本文から書いたものです。