FIDIC Red Book: works insurance

The Contractor has works insurance. Major damage is caused due to a design error by the design engineering team.
Should such loss be ( have been?) covered by the contractor’s works insurance or does liability lie with the design team?

Design is one of the Employer’s Risks which is deemed to be covered by the Works Insurance. So, yes, it is covered. The situation may be different if the design error was proved to be caused by negligence.