Make source files include-what-you-use

After the rework of #1928 the source code does not build, as some source files were using transient includes only, which might have been removed.

Fix up the source files in a include-what-you-use manner.

Directly include dependent headers in source files

So doing the whole codebase at once does not work. The scope is huge and very likely to introduce some errors. Therefore I'll debunk it into stages:

pre-tool work: stuff that must be fixed before running clang-tidy or clang-format with the sorting
clang tidy and header sorting by a small scope of changes which can be manually reviewed. (most likely going by directories one-by-one)

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