An extra delightful thing about Project Hail Mary is that, eventually, humans WILL go to Erid, and Eridians WILL visit Earth. And there's every likelihood Rocky will be there to see it.
For one, humans on Earth likely continued to breed astrophage, trying to minimize its range or damaging effects - any number of things. Rendering it sterile would be ideal, of course, but it was likely impossible until the mission succeeded. You can damn well bet your ass Stratt was out there chaining scientists to workbenches, trying to find or force a silver lining. She wouldn't be wrong: Astrophage IS an excellent source of fuel, which means it has great potential. PLUS!! the discovery of Taumeba gives you a way to control it.
Erid is only 16 light years away.
Imagine humanity pulled back from the brink, striving together to produce not one but TWO (at least!) huge joint efforts to save ourselves and each other. Project Hail Mary was followed the Taumeba Project, surely. The world comes together again.
I, however, like to imagine there was a third plan.
I think meeting Eridians became a worldwide obsession. Ryland Grace's legacy can be nothing but a collective triumph, though his contact with intelligent alien life is somehow second to saving the Earth and who knows how many other systems. Once saved, the next major project would surely be meeting our interplanetary friends. How would we say "hello"?
Let's say Earth's initial overture is a simple probe, Voyager style. What do you send? Well, they know Grace may still be out there, or at least was/is known to Eridian culture. He's the one link; the only common element.
The probe launches, and what it's full of is love for Ryland Grace. His childhood pictures. Interviews with his students. Thousands of statues and dedications and documentaries. Videos of worldwide celebrations of the Day of Grace. Kids' drawings of Rocky with laboriously-written thank you notes, thick with crayon so the Eridians can see. We love him too. We love you already.
Given their longevity, I imagine Rocky and Adrian opening the probe together, trilling over memories of their old friend. Stories they only heard about secondhand or not at all. Joy and triumph and thankfulness and hope, all in one small interstellar package. Amaze amaze amaze.
After all, it's Full of Grace.