"The style to which she has become accustomed" means "her standard of living." It's old-fashioned language that has become a joke. It occurs in Victorian-era novels. It might be used by a woman's father, talking to a man who wants to marry his daughter. It means "are you as wealthy as we are? Will you be able to maintain her standard of living?" It would be part of a number of question that amount to "are you our social equals?" It suggests that someone is paying close attention the financial aspects of the marriage.

Jmat is correct, I believe. There should be a comma after "me". The clause "to which she had become accustomed" modifies the word "style". "Thanks largely to me" is a parenthetical.

I think you might be missing a comma. The style to which she had become accustomed = 她习惯的款式.

thanks

It means "to keep giving her the things she has always had", the things she is comfortable with