Is it safe to say that because satellite DEMs are generated from satellite data, they suffer from similar error sources (perhaps, except instrument errors), so that, if one measured elevation from different satellites under the same conditions (e.g., weather), should one expect their errors to change together (i.e., increase or decrease together)?
Well, I doubt that there is any kind of correlation as the methods of aquisition differ... If you take the Japanese Daichi vs. the SRTM data they are produced with passive and active sensors. While Daichi offers super high resolution it "only" works with cameras and produces 3D data via Structure from Motion (like with UAVs or terrestrial imagery)... SRTM is a radar which is by far less detailed but can penetrate vegetation. Daichi offers a DEM clean of vegetation but thats a filtered product.
I think we cannot find overall correlations as Andreas suggested. However, there are in general topographic situations which are more prone to errors for the (often medium resolution) satellite DEMs. Especially incised river valleys or gorges in mountainous terrain can suffer from errors as the medium resolution DEMs might be unable to represent the small scale variations in topography. See also Schwanghart and Scherler (2017):