Is the wife considered sinful if she lives with her husband who takes an interest-based loan for a new project, and is that considered a reason to seek divorce?

If the loan is permissible (halal) and there is an intention to repay it, then there is no harm in it. However, an interest-based (ribawi) loan is forbidden (haram) and not permissible to take. "And whoever fears Allah - He will make for him a way out" (Quran 65:2). It is permissible to seek divorce or khul' from someone who consumes riba, but it is not obligatory, and it is valid to continue living with him while advising him. As for consuming from his wealth, if he has another permissible source of income, there is no objection. But if all his earnings are unlawful and there is no other source, then it is permissible to take from it only what is necessary, without extravagance, while continuing to advise him.