WARNING: The following contains major spoilers from Star Wars: The Rise of Skywalker and the first season of The Mandalorian.
Force healing: The ability to heal oneself or another by way of pouring one’s life energy into a wound, but at the expense of their own vitality. While it has made appearances in the past in Star Wars Legends, it made its first live-action appearances in two recent Star Wars productions: the seventh episode of the first season of The Mandalorian and Star Wars: The Rise of Skywalker.
Many arguments have been circulating since the release of the latter, and one of them has been about Force healing and how it hasn’t been used at all in previous live-action productions of the franchise. Apart from director J.J. Abrams wanting to incorporate it in for story’s sake, its appearance actually shows the shift in mentality between the Jedi of the past and present.
The Jedi who were alive before and during the Clone Wars were not in the right state of mind. They were arrogant and they were blinded by the Dark Side of the Force; so much to where they completely overlooked the fact that Palpatine was the same Sith Lord they had been looking for throughout the duration of the war. It’s because the Jedi had gone astray from their ways that it’s very likely they would have been incapable of performing Force healing — never mind knowing how to do it at all.

Luke Skywalker may have very likely learned how to conduct this ability; not from Obi-Wan nor Yoda, but from the sacred Jedi text found on Ahch-To, the birthplace of the Jedi Order. As seen at the end of The Last Jedi, Rey took the books to study from, and probably learned about Force healing the same way.
As for Ben Solo, it doesn’t seem like he was ever taught how to do it, for he had that facial scar up until Rey healed him in The Rise of Skywalker. Once it was established that he and Rey make up a Force dyad, he was able to perform the technique in such a major way because of Rey’s life energy already running through him.
Force healing appears to be a primal technique; one that comes from both a selfless place and a place of genuine care for the being that is in need of it. It would explain why The Child (otherwise best known as Baby Yoda) was able to do the technique on Greef Karga in The Mandalorian; he saw someone who was in need of help and despite being 50 years of age, he is still very young for his species.
Force healing and its usage mark a sign of the times in the world of Star Wars. While the Jedi who were killed off in Order 66 probably would have been incapable of using it, those who have followed since then are much more likely due in part to primal instincts or taking the time to learn from the original source.
Your explanation goes far in explaining this seemingly out of nowhere skill.