1) Reducing website bandwidth and computational usage (static sites, small images, reducing extra resource requests). Super common topic that HN talks about all the time.
2) Reducing the electricity bill for the server and powering it with renewable resources. This part is quite neat, I think, but for a single bespoke website, the energy savings of using a single low-power server seems pretty trivial in the grand scheme of things — I could get similar savings by changing a living room lamp to a more energy efficient bulb.
This inspires me to propose a third category of energy efficiency that the article doesn't touch on: human energy costs.
Humans are quite energy intensive devices, and I suspect that the labor and human-maintenance costs of making this website dwarf the direct energy costs of running a webserver. I'd be curious how one would go about optimizing these other energy costs, and whether that can be done in a way that still preserves quality of work/life for the humans involved.