So far so good.The road across the dam is damaged, the dam is not.
And I have seen reports that the rail bridge is ok for light stuff and the Russians have put wood over the rails for that purpose. But either they are alternating that with rail (which seems unlikely) or its not strong enough for rail
The reservoir behind that dam is enormous, it'd be truly catastrophic if it gets destroyed - for the devasting downstream flooding and then for the longer-term water supply and power impacts.

Kakhovka Reservoir - Wikipedia
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