What do we do if SETI is successful?

Get better camouflage so we don't get get found in the Dark Forrest. https://en.wikipedia.org/wiki/Dark_forest_hypothesis

>The name of the hypothesis derives from Liu Cixin's 2008 novel The Dark Forest, as in a "dark forest" filled with "armed hunter(s) stalking through the trees like ghosts". According to the dark forest hypothesis, since the intentions of any newly contacted civilization can never be known with certainty, then if one is encountered, it is best to make a preemptive strike, in order to avoid the potential extinction of one's own species. The novel provides a detailed investigation of Liu's concerns about alien contact.

Liu Cixin had to break the laws of physics -- badly, multiple times -- in order to make the Dark Forest game theory work. That's not a problem, fictional rules are good fun, but generalizing his conclusions back to the real world without sending them through a customs inspection first is a problem. See also: do the dinosaurs escape because the laws of chaos theory dictate that dinosaur zoos are mathematically impossible? Or do they escape because otherwise I wouldn't pay to see the movie and neither would you?

If we ground ourselves back in reality where the speed of light is probably law and the spooky aliens probably don't get to tamper the laws of physics, the actual game-theoretic winning move is always to grow voraciously, threat or no.

Where the speed of light is probably law (our universe) there is no way aliens could reach earth. The only possibly scenario where earth is in danger is if we terraform and colonize mars (Venus would also do, or a few other large rocks), then we have a falling out and start a major war. The few survivors would not know if anyone is on Mars, but if so they might still be out to get earth so better be quiet. If you are not already in this solar system you can't get here in a useful timeframe no matter how long lived you are.

We should expand our definition of Aliens visiting earth.

If we received a signal (at light speed) that described how to build a physical alien computer, and then ran a program on that computer, which happened to be AI, we would have alien visitors.