I cannot figure out how to change the elevation of the “ground” in the Background tab for Styles.
If you mean you want to move the default ground plane (coloured green in your top image) up, I don’t think you can. What you can do is to create your own ground plane (like a larger version of your bottom image rendered in browns) and move that around.
Or you move the model.
Aww too bad. Seems like a missing feature. I was hoping just moving the Axis would do the trick!
Maybe it would help to consider that the line between sky and ground is the horizon. If you were standing out in a place where you could see to the horizon without any intervening stuff like trees or hills or other buildings, how would you change the apparent height of the horizon relative to your house?
The horizon is the vanishing point of the perspective. It moves relative to the camera position and the Z-0 plane to show where a real horizon would be. You can move the home axis in SketchUp but that does not change the base model 0,0,0 point, it just makes a new working axis somewhere else. Even if moved it you can always click on the axis lines and choose reset, so the true model axis is never lost. You can move your house up or down to change its relationship to the horizon or use a style that does not have a horizon and draw your own ground plane (best).
I don’t see why it’s not fine to just move your model up and down. I usually don’t use the ground in a finished model anyway, modeling a ground to match the building site. Sometimes my model is hundreds of feet above this SketchUp “ground” plane (as a sea level reference). I consider it a handy visual to keep you oriented as you model.