This isn’t exactly what you are asking for, but in terms of seasonal storage, the ground is at least commonly used in district heating and cooling systems via borefields as essentially a thermal battery. Buildings reject heating into the loop during summer, and it then gets dumped into the ground at the bore field, and similarly, in winter the pull heat from the loop which comes from the bore field. Ultimately, this relies on the fact that the borefield is already essentially at the right temperature to start (which is pretty trivial to achieve at a depth of around say 200m). One caveat is that if you live in a heating-dominated climate (so cold and snowy), you need to inject heat into the ground so that that the net balance of the thermal demand on the year is unbiased. However, you could see a version of this where you actually just overcool your buildings in summertime when you have excess solar potential, and then pull that heat back out in winter and end up balanced. This strategy wouldn’t work in a cooling-dominated climate unless you have excess clean electricity in winter but not summer.

From the perspective of the grid, this would effectively be a form of seasonal storage, since you no longer need to spend any electricity to inject heat into your borefield for balancing purposes, and additionally, you would have lower DeltaTs in winter than you would otherwise so your heat exchanger efficiencies ought to improve.

Edit: It’s almost certainly a better idea to use proper batteries that operate on the timescale of a day to soak up the excess electricity during the day and reuse it during the evening peak, rather than use the excess to pump heat into the ground, but still, there might be at least something there if there is a need for truly seasonal storage…

Maybe I will try to run some sims of this kind of system sometime over the summer.