It's smaller, but not actually negligible. An old but oft-cited 2002 study said a laptop with a three year lifecycle took about twice the energy to manufacture as operate. Silicon is much more energy intensive than other materials, with fab energy consumption apparently relatively steady over time on the order of 1 kwh/cm^2 of silicon processed.
So, there is a high bar for replacing a computer with a new one to actually save net resources, but an actual 10x reduction in power consumption like replacing a P4 desktop with an RPi is big enough to pay off reasonably quickly.
I am even more interested in how the formula works out if you buy one professional laptop (say, Lenovo X13) with a Ryzen CPU -- because they consume less power -- and I am looking forward to reading such an analysis sometime in the future.
So, there is a high bar for replacing a computer with a new one to actually save net resources, but an actual 10x reduction in power consumption like replacing a P4 desktop with an RPi is big enough to pay off reasonably quickly.