When they mention tearing them in half, I’d imagine this more closely resembles what we would think of as slicing and just has the tearing effect due to the size of the material

You can probe different areas of the same device by adding many electrical probes, usually in a geometry called a Hall bar. In the old days of TBG, the different regions of the same device would do wildly different things. These days we are much better at stacking, and the different regions of the same device will be mostly the same.