Although I am not an avid user of this service, and my data is a bit sporadic, I have found the information provided there to be quite accurate. Alternatively you could use expertflyer, but this requires a paid subscription. Google's ITA matrix could also be of help if you are interested in specific fare(s).

I have heard from my preferred travel agency that ITA Matrix is unreliable when it comes to SAS (I had an itinerary planned using ITA Matrix but none were available).
However, so far bcd seemed reliable.

I was looking at availability on BCD (and another site non-public site) for SFO-CPH that is showing R class before Y, suggesting that it is in business. It was zero until around 48 hours before departure when business dropped from C9 D9 to C4 D0, but R became R3 and then R4 hours before departure. (So it shows C4 R4 Y4, etc...) This suggests to me that it shows availability for paid/ auction upgrades. What do others think?

Historically, R was a non-revenue booking class, which would never show up on any availability tools.

It sounds like a reasonable explantion, they do have to flag the inventory for paid upgrades somehow. I seem to remember that UA also used R to show space available for upgrades with GPUs, but as I never were a big United flyer and have only ever used friends' GPUs I am not the most reliable source on that.

I was going to say no regarding UA, but did a quick search. R is their new discount bucket for Premium Plus (their new premium economy product) and they have upgrades in RN for this. If you are talking about pre-CO merger then I suddenly have a vague recollection that they used R. But UA is not part of the Amadeus family either.

If my theory is correct, then it is surprising since SAS would normally not make this available in the public domain.

UA don't for sure anymore, now you can just look at the number of open J seats, and hope the count is equal or higher to your number on the upgrade list. But as long as you are using Plus Points (as it is now) you know any available J seat will be used to clear the waitlist. So all in all slightly different concept.