What is the ruling on agreeing to a divorce in exchange for each party taking what they brought in terms of furnishings, then this agreement is breached and everything is demanded, in the case of a marriage where intercourse did not occur due to the wife's phobia?

If the divorce is in exchange for each spouse taking back the furnishings they brought, then this is a divorce for absolution (ibra’) which waives the agreed-upon financial rights from the husband, because it is a type of khul‘. As for other financial rights, such as the mahr (dower), the wife has the right to claim them.