An N100 minipc or second-hand Dell Optiplex doesn't cost too much more than a rasp-Pi ($100-200), has a lot more power, and will only pull about 10W idle.

My optiplex shows as 8.191 kwh last month -> 11w average.

Is 10W idle the lowest one can reasonably get a small home server? As a comparison, that's about as much as my fridge draws on average. Also, a mechanism to maximize the time spent at idle would be useful. Basically all the optimisations done for phones.

yep yep n100s are great. I just use my gaming desktop as server, uses more money in power but it'd be on for hours a day anyway and i already own it, so i'm not concerned.