clang-tidy: Enable misc-include-cleaner check (#39835)

The previous commit fixes all remaining violations of the check for
a very specific setup (Fedora Rawhide with as many dependencies as
possible installed). The linter job in CI runs that specific setup
so we enable the check in the clang-tidy config but do not yet enable
the clang-tidy test suite in meson by default as it will very likely
still fail in different setups than the one in CI.