What you're describing is post-inflammatory hyperpigmentation (PIH) — excess melanin laid down where the skin was inflamed. It's more common and longer-lasting in deeper skin tones, and yes, it can genuinely take months per mark; that's the honest baseline, not a sign your routine is failing (review: https://pmc.ncbi.nlm.nih.gov/articles/PMC2921758/; overview: https://dermnetnz.org/topics/postinflammatory-hyperpigmentation).
Two things move the needle. First, sun protection — UV (and for some people visible light) keeps re-stimulating the pigment you're trying to fade, so daily broad-spectrum sunscreen is what lets anything else work; a tinted mineral formula with iron oxides adds visible-light protection that matters for deeper tones (https://pmc.ncbi.nlm.nih.gov/articles/PMC8887048/). Second, a pigment-pathway active used consistently: azelaic acid has solid evidence and is friendly to deeper skin tones (https://pmc.ncbi.nlm.nih.gov/articles/PMC12472904/); expect visible change on a weeks-to-months timescale.
Just as important: gentleness. Aggressive scrubs and strong peels can trigger new inflammation, which in PIH-prone skin means new marks — the treatment becoming the cause. If you want to exfoliate, mandelic acid is the gentle end of the acid family for exactly this reason.
If the marks are truly entrenched after several months of the above, a dermatologist can add prescription options. But most acne PIH does fade — protect it from the sun, treat it gently, and give it an honest season rather than an honest week.