"Landscape" is an ordinary, everyday word. It doesn't suggest anything precise. It doesn't suggest measurement. It doesn't suggest that you know heights in meters or distances in kilometers. It is more of an artistic or visual idea. It is the look and shape of a piece of land.
It can mean a big piece of land--the scenic landscapes of the Hudson River. In the phrases "landscaping" and "landscape architecture" it can also mean the aesthetic design of the land around houses and in public parks.
"Topography" is a rarer and somewhat technical word. It means the exact, precise measured shape of the land. A hundred years ago it would have been measured with surveying instruments. Nowadays it can be done with aerial and satellite photography. A "topographic map" has contour lines on it. It shows the precise elevation of everything on the map, and from it you can deduce the complete three-dimensional shape of the land. You can calculate how steep the grades of roads are, and exactly how many feet of elevation gain it would take to walk or ride a bicycle along a certain route.
The phrase "the topography of the landscape" isn't particularly common. I think that in this phrase landscape means something like "the shape of the land in a region of interest," and "topography" means "a detailed description of what that shape is." I suspect that "the topography of the terrain" would be a better choice of words--that is, I suspect that "landscape" is being used to mean "terrain."
So, you could say "The landscape of the Grand Canyon is spectacular. The topography of the terrain is rugged, with steep canyon sides. The geology of the terrain includes over forty sedimentary rock layers..." And if you wished you could say "landscape" instead of "terrain."