Keep the include paths clean and separate. We use directories to group source
files together. That makes sense (I guess), but then we should use this
grouping also when including files. Thus require to #include files with their
path relative to "src/".

Also, we build various artifacts from the "src/" tree. Instead of having
individual CFLAGS for each artifact in Makefile.am, the CFLAGS should be
unified. Previously, the CFLAGS for each artifact differ and are inconsistent
in which paths they add to the search path. Fix the inconsistency by just
don't add the paths at all.