This thing https://www.audiophonics.fr/en/diy-kits-and-boards/audiophon... is a C13/C14 block with a 3.5mm control. AC power on if 12V minimal current applied via the 3.5mm, otherwise off. I haven't got around to it yet but my sketchy DIY idea is power-over-ethernet into a splitter into that. That'll power off the server when the switch port is turned off.

Strangely I haven't found a relay in the same packaging anywhere else.