Sometimes simple ideas work, and this one is pretty simple.
Soil erosion occurs when rainwater lands faster than it can drain and starts to run off, and as it does, makes streams that wash away surface soil. It is worsened in heavy rain because the higher energy of the larger raindrops, which fall faster, breaks up the soil particles and makes them easier to wash away. Having excess non-draining water and a freshly broken surface layer makes for rapid erosion.
The speed of run-off can be slowed somewhat by making furrows run diagonally to a slope instead of straight up and down. Terraces also work, locally flattening areas of a slope and adding a small earth wall to keep water on that area until it can soak in.
My tiny idea is to imprint a waffle structure into the soil surface after plowing and leveling. If you aren’t familiar with waffles, here’s a pic from wikipedia. I don’t recommend adding the strawberries.
Waffles would keep rain water within a small square and prevent the soil from washing away, at least until the waffle floods and overflows. Some wall breakage would then occur, but much more rarely than otherwise. I don’t think the waffle structure needs to be printed very deeply. Even a few millimetres of wall would make a difference. Intuitively, I imagine a typical waffle could use a 10cm grid with 1cm wide walls 5mm high, but I haven’t done any experiments to determine the optimum. At that structure, soil compression damage would be minimal and local confinement of organic materials and water would work fine.