I don't think Anne gives herself no credit or suffers from lack of self-esteem as far her as talents are concerned. She knows she is intellectually superior to the Musgroves re chap 5 -- she had a "comfortable feeling of superiority" and "would not have given up her own more elegant and cultivated mind for all their enjoyments". She also knows her own capability e.g. that she had to take charge when her nephew broke his collar bone in chap 7, his other aunts were "frigtened, enquiring companions", rather than "useful assistants".

I think what Anne suffers from is lack of confidence in her own physical attractiveness. Her father regarded her appearance as "haggard", and after being informed of Wentworth's ungallant remark in chap 7 that she was "so altered he should not have known [her] again.", it must have confiremd ot her that she has lost all her looks and could no longer attract any man. But that began to change at Lyme.

Capt Benwick liked her company, but that could be for discussing literature (chap 11). But in chap 12, a strange gentleman "looked at her with a degree of earnest admiration which she could not be insensible of ... her very regular, very pretty features, having the bloom and freshness of youth restored by the fine wind". She alter nearly ran into that same gentleman in the inn "and this second meeting, short as it was, also proved again, by the gentleman's looks, that he thought hers very lovely ... Anne felt that she should like to know who he was." He turned out to be her cousin and the heir to her father's baronetcy, but they did not know that then.