Separate public and private headers

[NikitaZotov]

• [x] Read PR documentation
• [x] Update changelog
• [x] Update documentation

This PR unblocks tasks for build system improvement.

Related tasks:

• Remove configure_file for tests and use target_compile_options

Links:

https://www.reddit.com/r/cpp_questions/comments/m7k0bs/project_structure_in_c/?rdt=43314 https://slaptijack.com/programming/project-structure-for-cpp.html https://www.linkedin.com/pulse/what-general-c-project-structure-like-herbert-elwood-gilliland-iii/ https://hiltmon.com/blog/2013/07/03/a-simple-c-plus-plus-project-structure/

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 94.28571% with 2 lines in your changes missing coverage. Please review.

Project coverage is 95.56%. Comparing base (af18f99) to head (61a587c). Report is 18 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #404 +/- ## ========================================== - Coverage 96.24% 95.56% -0.68% ========================================== Files 219 224 +5 Lines 23224 23454 +230 ========================================== + Hits 22351 22414 +63 - Misses 873 1040 +167 ```