I‘ve not been as active recently so i might be missing something that has already been discussed went over and I would need to reread some chapters, but I don’t actually think that we’ve learned anything new from Mihawk about CoC and Haki that Ray didn’t teach Luffy right in the last chapter before the timeskip where he gives his explainer on what it is. Ray says it’s to feel no doubts, Mihawk says it’s a sense of self, Haki literally means ambition/willpower.
It seems to me that is pretty much all the exact same thing. It’s just basic self belief and drive.
I don’t think that Big Mom was lacking in any of that tbh. Big Mom was highly ambitious, she was hugely successful and she was powerful. I understand that she did not know everything that happened to her in childhood, but I don’t think that knowledge of events is the same thing as the self belief that Haki is made of. She has concerns over where Carmel went, but she seems to have still used that as an inspiration for her dream to make a world that Carmel would have liked (in BM’s opinion). If anything Big Mom learning that she killed Carmel and her friends would probably make her Haki weaker if anything.
Honestly I just think the Zoro CoC plotline since Wano ended is poorly written and Oda needing to put the brakes on him because he made him too strong on Wano. It’s basically Zoro’s version of Luffy’s stamina issues coming and going when the plot demands. Oda’s literally admitted to it being something he struggles with.