As far as United is concerned, United has had a bit of a fight with SAS connections lately because United wants to get rid of the responsibility for transfer pax who get delayed in the USA. Don't think it's necessarily connected to the alliance change.
Because of the CPH flight arrival and departure times and UA ground staffing levels/hours, UA has long had more issues with how to handle transfer passengers in the transit baggage area at ORD T5 and also the transfer passengers at ORD T1/T2. But it has gotten worse the last several months as UA agents at ORD seem more overwhelmed in the evening hours than used to be the case. However, with SK and UA both looking at a future next year where SK won’t be with Star Alliance, SK needs to get other arrangements in place because there will still be lots of transfer passengers and transfer luggage to deal with for several months even after SK gets out of Star Alliance. It’s a good thing that SK and UA are both aware that things will change and they need to get ahead of issues that will hit with the transition. But these issues are not unique to SK and UA at ORD, so there should be similar developments also going on at other UA hubs with SK service.
For several weeks now, I can no longer find any SK award space on UA app/site when trying to use UA miles. The SK award space is there using points from all other Star Alliance programs which I use, but not with UA miles.