GR predicts the wavelengths would shift longer; NOT redder. To appear redder , one needs more red or less blue or both after the shift. The shift to longer wave lengths causes the existing red to disappear. The existing blue to now be red and some shorter wavelengths to now be blue. Thus to shift red there must have been more blue than red initially . But that implies that there were more shorter wavelengths than lower in the first place , so there should now be more blue, not red.
Took me a while to find the answer to why red. Every particle has three mass states. The photons 3 are no mass, one unit of mass and a lot of mass, the W particle. The one unit of mass is the one that curves the direction of light as it pass a star. Now this star is in the gravitation stronger beam as it is in between us and the center body. Thus those photons are subject to a lot more gravitons; and those photons pick up the one extra mass unit allowed and thus slow down. That slow down requires more time in passage and a longer time to get here and thus ages more, shifting more higher wavelengths from blue to red.
https://www.independent.co.uk/news/science/star-black-hole-einstein-relativity-proof-light-a8466041.html
"Scientists have watched a star as it sped past a black hole, lighting up one of the mysteries at the heart of the universe.
The unprecedented view of the dramatic behaviour was not just an exciting peek into the universe. It also confirms for the first time that Einstein's predictions about what happens to a star when it passes near a supermassive black hole are correct.
Einstein's 100-year-old general theory of relativity predicted that light from stars would be stretched to longer wavelengths by the extreme gravitational field of a black hole, and the star would appear redder, an effect known as gravitational red shift."