Why was the Battle of Mu'tah called a "ghazwah" (expedition/campaign) even though the Prophet, may Allah's peace and blessings be upon him, did not campaign with them?

The Prophet’s (peace and blessings be upon him) endeavor to fight the disbelievers himself or by an army he dispatched is called a "Ghazwah." The word maghāzi is the plural of maghzā, and it refers to what the Prophet (peace and blessings be upon him) undertook by intending to confront the disbelievers himself or by an army sent by him. Therefore, naming the Battle of Mu'tah a ghazwah is correct, as its army set out by the Prophet’s (peace and blessings be him) command and under his supervision.