[Feature request] Python-like interface for modern C++

#4894 proposes to expose C++ headers to 3rd-party applications. As an extension of #4894, we should also consider building a Python-like frontend in modern C++. I'm thinking something like https://pytorch.org/cppdocs/frontend.html#end-to-end-example, where PyTorch offers a complete modern C++ API that's at feature parity with the Python package.

In particular, features like early stopping should be available from a C++ application. Early stopping is currently only implemented in the R, Python, and Java wrappers.

Once the C++ frontend is introduced, we can make some stability guarantee about the frontend. That is, the frontend would change more slowly than all other C++ classes (considered "internal").

@trivialfis