What do we do if SETI is successful?

That's not how electromagnetic radiation works.

Efficient communication looks like noise.

It kind of is. You're thinking directionality, but there's also the fact that optimal transmission will involve using compression and possibly encryption, which by its nature turns the signal into noise if you don't already know it's a signal. An optimal signal, which it seems reasonable to assume would be what aliens would be using by the time they're communicating across star systems, would be much more difficult to detect as a signal than something like an FM radio station, which puts a lot of energy into broadcasting a carrier that is there even if the station is transmitting total silence.

You're forgetting the Contact method where the actual signal is buried in a beacon signal. The beacon signal is very much a "primitive" non-random not noise signal...primes. Now that you've recorded enough of that beacon signal, someone analyses each of the pulses to realize there's a message embedded within. This way, you don't need a response to know someone go it. When they magically show up in the machine you've sent the plans as that message, you'll know the message was received.

No, I'm not forgetting fictional cases in which the point was to transmit to an unknown civilization. I'm talking about the real way that real civilizations are going to transmit data to each other, without meaning for it to be picked up randomly, on the assumption that while aliens may or may not have human-comprehensible motivations we can generally operate on the assumption that they will not be stupid and wasteful in the pursuit of their goals.

This isn't quite why I wrote this, but it's close enough: https://jerf.org/iri/post/2023/alien_communication/ If we're going to argue in the form of fiction.

We sent a gold plate with a bunch of data on it hurling through space on the off chance that a) it is ever found, b) it is found be intelligent beings, c) would figure out the little puzzles. In this case, the beacon would be the satellite itself even if its power has long since died and no longer emits any RF energy.

It's not actually sci-fi. They sent a message with Arecibo that was also encoded if not within a beacon signal. Just because it was a scifi plot does not mean its not something that could be done to good use. If humans wanted, we could send a similar beacon signal even if it's not pulses of all the primes between 1-101 with the same data from the gold plate.

At one point, flying like a bird was scifi. Traveling to the moon was scifi. Having a computer that fit in the palm of your hand was scifi. There's a lot of actual science that has been inspired from a scifi idea.