Does a divorce that the husband made conditional on his wife's talking to men occur based on his intention in defining the type of men whose conversation is forbidden? And is the wife sinful if she talks to a man out of necessity and without the intention of betrayal?

The Fatwa (definition)'s Summary:

A conditional divorce takes effect when the condition is met, according to the majority of scholars. The reference for determining the condition is the husband's intention. If your husband intended to prevent you from speaking to men in a specific manner, then his oath is confined to that manner. He would not be considered to have broken his oath if you spoke to a man in another permissible way out of necessity. It is important to note that it is not permissible to respond to the husband's sin with a similar sin. Moreover, the husband's forbidden relationships are religiously reprehensible, not merely because they constitute a betrayal of the wife.