Re: "the chase" Reprucussions
The Klingon and Cardassians quickly left orbit, probably forgetting what that message was about and returning to their home worlds. Probably the contents of the message was stored away by the Federation and Romulans in some database somewhere.
Interesting that only the Feds and the Romulans "got" the message. As someone else suggested, maybe there are other such "messages" embedded in our DNA - Perhaps to a super-weapon or some other ancient knowledge. I could imagine a whole Tal-Shiar division attached to discovering such a secret. Perhaps stories to be told lie in that direction...
One day soon, man is going to be able to harness incredible energies, energies that could ultimately hurl us to other worlds in... some sort of spaceship.