Yes! Exactly this! I would ALSO love this concept where Obi-Wan does forgive him because he HAS to in order to let go of the pain and anger, but that doesn't mean that anything has been forgotten and that the damage Anakin did to their relationship can be at all fixed.
I have an entire AU in my head (based loosely on a fanfic I love) where Padme lives and manages to capture Anakin in an attempt to "save" him, but neither she nor Ahsoka nor Rex are able to actually get through to him and so they bring in Obi-Wan to see if Obi-Wan's able to actually do anything, and... it works. Not quickly, not immediately, but it works.
I know there's lots of reasons why Obi-Wan theoretically shouldn't be able to ever get through to Anakin, there's narrative thematic reasons for why it could have only ever worked with Luke, but Luke is like 5 years old in this AU and Anakin is stuck in a cell with no way out other than to sit there and talk to Obi-Wan and convince Obi-Wan that he's stable enough to be trusted with people's lives. And I am still convinced that Obi-Wan was the ONE PERSON that we ever see Anakin actually willing to be selfless with (other than Luke later, just that once). Obi-Wan is the ONE PERSON who truly manages to get through to Anakin, the ONE PERSON whose opinion of him matters enough for Anakin to not just do whatever he wants when he's angry. There's MULTIPLE moments in canon to back up that Obi-Wan's relationship with Anakin was the healthiest Anakin ever had and that Obi-Wan had a capacity to get through to Anakin in a way no one else really did. And above anything else, Obi-Wan was Anakin's guide. That's what a Master is, a guide for their student to figure out how to walk their own path. And that's what Anakin needs in this moment, he needs a guide that he trusts to show him how to get back to a better path.
And so, in this instance, it works. It works because it HAS to, because none of them have any other options and they're unwilling to just give up, so they push through the pain and the anger and the betrayal and the fear and it takes months, it takes over a year, but Anakin finally manages to come around. He's not the nicest person in the world, still, he's still a little quick to anger and has shit to work on, but he's not completely consumed by darkness anymore and he's willing to turn against Palpatine at least.
And once Palpatine is dead, they go their separate ways. It's the last lesson Obi-Wan has to teach Anakin, how to let go. It's the most important one, too, the one that got Anakin in trouble last time. Obi-Wan isn't dead, but the pain Anakin caused will probably always remain. Obi-Wan will never be able to look at Anakin again without remembering the bodies of the younglings covering the floor of the Temple and the smoke rising from the towers and the feeling of all the Jedi in the galaxy dying all at once and having to make that message saying that the Jedi's time was done just to save what few survivors might be left. Anakin will never again be just the little boy Qui-Gon picked up from the desert and left to Obi-Wan to train. He'll also always be the man who betrayed Obi-Wan and destroyed everything Obi-Wan had loved. And Obi-Wan does still love the boy he trained, but he can't continue to live alongside the man who betrayed him. He has to walk away, and Anakin has to let him. It isn't easy for Anakin, who has struggled SO SO MUCH with letting go, to recognize that Obi-Wan loves him and is proud of him and trusts him but doesn't want to be around him anymore. It's so hard to accept that this isn't something that he can fix, no matter what he tries.
But Obi-Wan guides him one last time, and Anakin lets him go and they never see each other again.