text: Checked today and signage is showing it as the signed route to the car parks (although parking is now prohibited)
  
  Road layout is similar to that in Hockey and Exhibition Road in London - both of which are mapped as highway=living_street - while these might not quite meet the Dutch standard of a living street they probably more accurately describe the road layout now - they look pedestrianised even though they take through traffic.  Castle Place, Road, Gate, and Hounds Gate have no additional restrictions on them so should arguably match?