Oh, my. I could make several places I saw that discussion centered right on this. That the prophecy made Anakin a weird figure now in the lore. It felt extremely out of nowhere.
Anakin was treated extremely poorly and his whole role was derided, his romance unbelievable and poor chemistry with the other characters. Rey got it bad too but Anakin was treated awfully as well. Both are horrible ways to treat people.
Back to Burnham. I think she was a tragic figure, shown not fitting in and not healing from trauma but forced to repress it under logic. I don't think she was supposed to be likable but sympathetic on her healing journey.
I recall people taking issue with Anakin for various reasons, as I mentioned before, however, I don't remember much griping about him being the Chosen One, or people not decrying the prequels being about him, his journey, like I do with Burnham.
To be fair, the nature of storytelling is different for the two franchises, and Discovery was trying something different, or making a franchise lead character more explicitly the lead whereas older/predecessor series were more subtle with it. And that might have thrown people off, but even, during the unsubtle days, there wasn't much griping either about the other leads from Kirk on saving the day, repeatedly.
And I didn't get that about Anakin really, for being the Chosen One. Yes, I saw people disliking the acting, the writing/direction, the romance, but not that bummed about him being the Chosen One itself. I can only speak on what I remember, and I don't remember the focus of prequel anger being about that. As I said before, I preferred Luke in that role, but Lucas made the decision, even though Disney suggested it was Luke anyway on Rebels years later.
Likable is so subjective. Burnham's tragic backstory and being sympathetic was part of the writers attempt to make her likable. Tying her to Spock, her spending time with Sarek and Amanda, establishing her as brilliant and courageous, a future captain in the making, her mentorship of Tilly, the doomed relationship with Ash, her reclaiming and advocating Federation values, all of those things were meant to sell her as a character the audience was supposed to root for. Some in the audience just didn't, and it goes that way sometimes.
I am iffy on Burnham as a character myself. I liked SMG's performance, but I didn't like how the character was always written. And I didn't care for making her Spock's sister. That being said, I never saw her as a Mary Sue or "Space Jesus", but I do think the writing was clunky at times and the writers needed to lead with action more than just people talking about how great the character was. Enterprise did this to some extent with Archer as well, so it wasn't just a Discovery "problem".