Seriously, I doubt it would even take that long. We get used to shit so quickly, and the news cycles have to keep feeding us new things, the only way we’d keep talking about the aliens if they kept doing new and interesting things. I’d be willing to bet a year later there would be some people who straight up forgot about it. “Oh yeah, aliens! Are they gonna, like, visit at some point or just keep exchanging calls with the Whitehouse?”
The speed of light is so slow as to make communication difficult. The best possiple case is they are about four light years away meaning a round trip question and answer is eight years. That is best case and those stars are generally thought to not be likely to have life. 20 light years gives the first possibility of life.
Which is to say we will never establish communication as you think of it. Instead we become aware of each other and send what we guess is of interest. maybe we ask questions but odds are a question sent is no longer relavent by the time we get an answeri
even the above is a best possible case. If we become aware of life there, is a good chance it is extinct long ago but evidence is just reaching us. The universe is that large*