Enable Clang builds in CI

[stv0g]

Once we have #920 merged, we should test Clang builds in the CI to avoid breaking them again.

[pjungkamp]

We don't necessarily need full clang builds.

Adding clang-tidy to the GCC build would effectively verify both since clang-tidy builds its AST using Clang's frontend. We'd get diagnostics from both.

Adding -DCMAKE_CXX_CLANG_TIDY=clang-tidy to the nix build should be all that's needed here.