Trees alone do not absorb much CO2 past the lifetime of the tree. In the vast majority of the world they die, decompose, and release a lot it again. To store this carbon (and energy) long term the material needs to be buried. Mangrove forests are excellent at this because anything that dies is quickly covered by sand into an anoxic environment where it can't be broken down by bacteria that create CO2. Over a few thousand years the sand layers really pile up. Over a million or so it'll turn to sandstone and coal/oil/methane). Hopefully a shale develops overtop or that methane is just gonna escape straight into the atmosphere anyways.
Melting eutectic salt isnt much more useful. Once you have molten salt, now what? Bury it? It will equilibrate with the ground. You might as well have just let the ground absorb the energy and saved the trouble of making panels.
Fun fact: Not all life on earth is a direct result of the sun's radiation! Sulphate reducing bacteria are regularly found in ocean floor vents and deep in caves, completely independent of solar events.