[cogman10]

Mobile phone SoCs would likely be the way to go for the best processing per watt.

The problem really is one of "how much is enough" more than anything else. Assuming someone wanted to really optimize something like this, a specialty built ARM cpu with lots of cores at a low frequency would likely provide the most ability to act as web server with a small power budget.

Such SoCs, AFAIK, don't really exist. You don't need a particularly fast CPU for web service stuff. You certainly don't need all the mobile extras (AI chips, GPUs, etc). What you need more than anything is core count.

[usrusr]

If you wanted to go full data slapstick you'd set up an elaborate protocol on the ISM band between a cluster of Nordic nrf52 or similar where each SoC serves exactly one page from its flash memory. Want to update the about page? Flash it on a spare board, connect it to the battery and disconnect the old version.

It will have awful latency, likely suffer hard from the shared medium if ramped to nontrivial loads, but it will hardly use any power at all.

And it will drive people nuts who know even the tiniest bit about computers, but those who don't will understand it just fine: "I disconnected that new about page and plugged the old version back in"