FYI, I think this is the central point of this test reported. "Einstein's general relativity predicts that bound orbits of one object around another are not closed, as in Newtonian gravity, but precess forward in the plane of motion. This famous effect — first seen in the orbit of the planet
Mercury around the sun — was the first evidence in favor of general relativity," study co-author Reinhard Genzel, director of the Max Planck Institute for Extraterrestrial Physics in Garching, Germany, said in a statement. "One hundred years later, we have now detected the same effect in the motion of a star orbiting the compact radio source Sagittarius A* at the center of the
Milky Way," Genzel added. "This observational breakthrough strengthens the evidence that Sagittarius A* must be a supermassive black hole of 4 million times the mass of the sun."
I have this Mercury test in my trusty Einstein book, Relativity, The Special and The General Theory, A Clear Explanation That Anyone Can Understand, 1961, p. 126. On page 103, "On the basis of the general theory of relativity, it is found that the ellipse of every planet round the sun must necessarily rotate in the manner indicated..."
Looks like confirmation of this prediction from GR rather than Mercury observations in the solar system without other solid measurements too. It is detecting this same effect in the motion of a star that is important. Moving in the direction of GR becoming a law of science vs. theory