Seems like the only way Russia will actually pay for the damages if they think they'll be keeping it.

It would be quite the win if Ukraine manage to take the territory back even partially rebuilt. We know that Ukraine have a policy of avoiding costly difficult offensive operations into obvious hard points and cities (selecting to go around instead). I imagine, all going well, if they were to find themselves in a position to liberate the Azov coast then they would try and set the conditions for a Kherson style Russian 'nope' retreat to avoid an encirclement.