Eventually all surface water will disappear underground or evaporate in the solar wind before the red giant subsumes the earth.

Would you send dna throughout the galaxy prior to that end?

The earth goes through dramatic changes on a regular, though extremely long, basis. The only difference between us and the dinosaurs is that we have figured out the history and have the capacity to worry about things we cannot change. They just went about their business until they were disappeared. But the results were the same. They are gone and someday we may be too. The universe works that way.

Wonder how many unexpected factors will step in to the breach during that time??