Is it legislated for a man to say to another man when bidding him farewell: "May you be in the care of Allah and His angels," or "May you be in the protection of Allah and His angels"?

There is no objection to the supplication "fi hifdh Allah" (in the care of Allah) and similar phrases, because Allah is the Preserver, and His angels preserve His servants by His command, as confirmed by His saying, the Almighty: "For him are successive [angels] before him and behind him who protect him by the command of Allah." The preferable option is the supplication transmitted from the Prophet (peace be upon him) when bidding farewell, such as: "I entrust to Allah your religion, your trust, and the consequences of your deeds," or "In the care of Allah, and in His protection. May Allah provide you with piety, forgive your sin, and direct you to goodness wherever you turn."