I have created a scene by duplicating another scene (using the Link Object Data option). I would now like to unlink some light sources. I have tried right-clicking them in the Outliner and clicking on Unlink, but it did not help - changing the strength of the light in the duplicated scene also changes the strength of the original light in the original scene. What am I missing?
I think your problem is the following one:
Unlink in the Outliner will unlink the object from its Collection, not from its duplications.
A linked duplication is a complete other thing than an object linked to a collection. To link-duplicate an object (make a copy that will follow all the modifications on the original), you need to press altD instead of shiftD.
To unlink a duplication, i.e. make it single user that won't depend on its linked duplications, select your object, go to the header menu > Object > Relations > Make Single User > Object & Data, then select Selected Object.
The problem is that it will also unlink from the objects of the same scene (maybe there's a way not to but I don't know it).