Esther needed to stress “and do not eat” after telling the Jews to fast in order to prove, as the Yalkut says, that the decree against the Jews was punishment for their sin of attending Achashverosh’s feast.
To explain this, R’ Shlomo Kluger tell a parable about a pauper who stole. He was caught and fined a lot of money. The thief told the court, “The money you are fining me is little to you, but is a lot to me. Perhaps you wouldn’t mind foregoing it…” The judge answered, “The fine we imposing is not for us; it is for you. The fine is meant to teach you a lesson.” Esther is therefore telling the Jews not to eat because it is meant to teach them a lesson.
R’ Elisha Gallico tells us “don’t eat” means even at the Seder, since this fast would include the first day of Pesach.