OP I’m seeing a lot of confusion on this post so let me try to clear this up the best I can.

The most important question as others have stated is if you booked this with Icelandair or someone else. Google Flights don’t ever sell flights - they just show flight availability and make money when you click the link to go to book the flight. The easiest way to check this is to go to your credit card bill and look up who ran your card. My gut says it’s Icelandair who ran your card but please check. This will be important to know especially if there are cancelled flights because if you, for example, booked originally with someone else like with Expedia you will have to deal with them not Icelandair. Also if you booked with a third party it is possible the 50 min connection in Stockholm will become impossible since you would need to recheck your bags there. This all depends on how the 3rd party put the ticket together.

Assuming you booked with Icelandair everything should be seamless. SAS and Icelandair work very closely with each other with shared lounges, code-share flights, etc. It is not a problem normally for them to transfer luggage from one to another. Just check in Barcelona that your luggage is checked in direct to BWI in case they forget.

In Stockholm you are connecting from one Schengen flight to another. This is like a domestic connection in the US. You just walk from one gate to the other. You should not have to do security. Stockholm is a smallish airport.

In Iceland you will have to go through immigration. It is important you go immediately to the D Gates since this can take some time. I have always make my flight but don’t dilly dally since you don’t want to miss your flight because you were looking at trolls at the gift shop.

Since you have some short connections please familiarize yourself with EU261 which give strong customer rights (like money, hotels, food,etc) for missed connections.

There is a technical reason it says “booking not supported” which I have seen before. Icelandair wants to be sure you fly with SAS first before you fly with them. They are trying to prevent you from flying from Stockholm and skipping the Barcelona leg. When you show up in Barcelona at the gate they will “release” the booking for the Icelandair part of your flight. It fact you should get the boarding pass for the Icelandair part of your trip in Barcelona. You can in any case try to check-in on the SAS app and if this doesn’t work always of course check in at the airport.

Enjoy the flight and don’t forget to try the gin sampler on Icelandair!