The only Delta Sky Club outside the US is located at Tokyo Haneda airport. Other than that, you will only find partner, a handful of Skyteam jointly operated lounges, and third-party lounges. Delta dropped access to third-party operated lounges many years ago for DL Gold+ Medallions (DL Skyteam ElitePlus) when flying international Delta metal. You must be flying in the Delta One cabin for access to third-party operated lounges when flying Delta metal. As the two BCN lounges are third-party operated lounges, you won't have access to these when flying Delta metal unless you are in D1. Skyteam partners continue to offer access to third-party lounges to Skyteam ElitePlus members (including DL members) in any class of service if you are flying on their metal on international flights.

Unfortunately, the Skyteam lounge finding can provide misleading information and the Delta lounge finder is generally more definitive (provided you set the correct filters) -- https://www.delta.com/us/en/delta-sky-club/locations
As you can see, there are no lounges available in BCN for DL Skyteam Elite Plus when flying DL metal and you are not in the D1 cabin.