Is it necessary to mention the details of the threat made by the victim, even if the other party did not hear it, when giving testimony?

The threat of a complaint does not affect the investigation. If the complainant's words included insults and slanders against the aggressor, then this must be testified to, because the complainant has fully asserted his right, and responding with insults is a form of asserting a right. If the right was not fully asserted, then the punishment may be lifted or reduced. The religion of Islam commands justice for all.