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> Agreed, e-fuels seem to be far and ahead the front-runner.

For covering Dunkelflauten? Yes.

For seasonal storage with a prolonged discharge (so, low power/storage capacity ratio)? I think thermal storage wins there.

Sure, thermal is great where it's possible. But there aren't that many places where district heating is viable.
I'm not talking about district heating. I'm talking about high temperature storage for conversion back to electricity. Round trip efficiency could be around 40%, better than green hydrogen burned in combined cycle plants.
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I just don't see it with thermal. You have to pay the Carnot tax, and you also need humongous amounts of material.

E.g. 100 GWh (4 days of 1GW thermal power) with a 100C temperature swing (you can't go down all the way to room temperature) will need around 3.6*10^4 tons of sand. That's a lot.

Honestly, power-to-gas sounds like the only reasonable way for now. In theory, with SOFC (Solid Oxide Fuel Cells) for power generation, it can beat the steam cycle.

The temperature swing can be much greater than 100 C. Heat can be extracted as a wave passing through the store, then heat added back by reversing the flow. It would operate like a counterflow heat exchanger.

View another way: if we hook several piles in series, then lukewarm air from a first mostly discharged pile can be directed into later piles for more heating. In the continuous limit this is the concept I described above.

> The temperature swing can be much greater than 100 C.

No, because your steam will be at a lower temperature as you draw down the heat, bringing down efficiency.

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That is wrong, and I already explained why.
36000 tons... doesn't actually sound like that much? That's a ~30x30m cube of dirt.

But I have no reference for the cost of setting up such a storage and how it compares to battery or hydro.

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The cost of putting dirt in a pile is $1-2/ton.
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The biggest expense will be the pipework inside that pile. That you won't be able to service easily. And you'll also need a LOT of insulation around it to prevent heat from leaking out too quickly.
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The insulation is just more dirt.
Homework: compute the heat flux from a 40 meter radius sphere, given the surface temperature 600C and the ambient temperature 0C. Now compute the amount of insulation needed to keep its temperature above 500C for 3 months, given that dry sand has an R value of 0.25 W/mK.