
There have been calls for an interstellar probe although that would of course be an incredible effort. Here is a bit more on that notion from wikipedia:
The announcement of the planet’s existence sparked renewed interest in Alpha Centauri as a potential target for an interstellar probe, including enthusiasm from mainstream astronomers.[16][20]Debra Fischer of Yale opined that “If you were going to send a spacecraft anywhere, or a probe anywhere, that’s where you’d go first.” A representative from NASA’s Innovative Advanced Concepts suggested several theoretical technologies that could make the voyage to Alpha Centauri in a few hundred years, including antimatter rockets and explosive nuclear propulsion.[20]
Planetary scientist Greg Laughlin admitted that such approaches were “speculative and farfetched so far”, and noted that with current technology a probe sent to Alpha Centauri would take 40,000 years to arrive, but expressed hope for new technology to be developed to make the trip within a human lifetime.[27]
Well that is a bit too long 😉 Perhaps even listening or sending S.E.T.I. signal would make sense first?

Yes we should!
Why
Yes, there is life in other planetary systems. That doesn’t mean it has to be intelligent.
Exactly some people can’t get the image of little green men out of their heads , and who knows maybe there’s other forms of life that don’t breath oxygen or water , life breads amazing life forms
Should the Centauries be looking for evidence of intelligent life here?