The best option for you is to treat the payment as a reduction in the basis of your home.
When you sell your home, most or all of the gain will be excluded from tax, so it is likely you will never pay tax on the income.
If you report it as rent, you will have to pay tax on it.
You can't know the cost basis of an old sidewalk or a tree, but it is reasonable to assume that the state is not paying you more than the damage is worth.
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