The aspect ratio of 1280 x 720 pixels is 1.77, while the aspect ratio of 2048 x 1536 pixels is 1.33. When you set the anchors to fullscreen, the Spine widget is given some size by Unreal Engine, like in your screenshot. It tries to best fill that size by "embedding" the skeleton bounding box inside the given area. If the aspect ratio of the area is not the same as the skeleton bounding box, you get what you see.
The widget can't really decide itself to stretch out so the full area is covered at the moment. Your suggestion of adding a fill mode property makes a lot of sense.
I have opened an isuse for this suggestion here:
EsotericSoftware/spine-runtimes2416
We've just started porting our new phsyics feature to all runtimes, which will take a while. I'm afraid I can not work on this in the immediate future. You may try to modify SSpineWidget.cpp
yourself for your use case for the time being.