@monsieuricon This is a thing, except not usually buried. Search for "non-pressurized hot water storage tank". I have a friend who has one in conjunction with his geothermal system. It has something like 4" thick styrofoam walls.
Sometimes there's a heat exchanger in the tank, and sometimes the heat exchanger is outside the tank. My friend's geothermal system uses the external geothermal heat exchanger for this purpose, so the tank is really just a styrofoam box. His is a rectangular prism; some are cylindrical.
Just keep it completely separate from your plumbing system; these energy storage system hot water tanks can get some fairly nasty bacteria growing in them that stay alive at unreasonable temperatures.
Something a bit like this has been in operation in Helsinki since 2018.
https://www.helen.fi/en/news/2018/underground-heating-and-cooling-plant-utilises-waste-heat
@monsieuricon The district heating in #Helsinki has a 320 million liters heat battery in a cavern. https://www.helen.fi/en/news/2021/gigantic-heat-caverns-in-mustikkamaa-filled