Why this eclipse could prove Einstein was correct

Geneal Relativity is quite close to "settle"[1]. Perhaps it will get a small corrections at very high or very low gravity values, but nobody found them yet. It's important to verify[1] it in new scenarios, but nobody expects something interesting. But if they find something interesting, they get a Nobel price, so let's try.

[1] not yet falsified, if you want to get thecnical.

The science is never settled. That's practically the Popperian definition of science, which is pretty much the accepted definition of science. You see this in the context of GR in, e.g., the galaxy rotation problem.