The South Schleswig Danish minority have been mentioned in every new year’s speech I can remember. It’s basically part of acknowledging everyone who feels ties to the kingdom of Denmark. Near the german border there is a danish minority in Germany and a german minority in Denmark. And to my understanding as someone not living near there it is a respected cultural thing on both sides. It is not something about laying claim to it. In this particular speech the very next sentence is about the king and queen feeling just what you quoted during their visit those places that year and how they are looking forward to visiting the Faroese islands. For context the king was crowned in 2024 so this was commentary on the first royal visit of the new reagents.

As others have pointed out they have valid grievances and good reason to want independence. As a dane I only learned about the non-consensual and secretive implantation of UID’s in women and girls that had been going on a few decades ago. Learning about that and other systemic issues they have dealt with I can not begrudge them wanting independence. Whether they seek it or decide to stay, I hope they have a brighter future ahead of them and that Denmark will support that as best we are able.