Enable headers sanity check build in lhcb-master

Already done in lhcb-gaudi-head, this change triggers a build of all public headers in isolation to make sure that public headers do not have hidden dependencies.

After I fixed all failing headers, new MRs are introducing new problems. Testing the headers in lhcb-master (and possibly other slots) is the only way to keep them clean.

This cannot be merged before lhcb/LHCb!4479 (merged)