My opinion is the poet isn’t physical eating poetry he’s using eat to show the consumptions of the poetry as he would with food he’s using eating to show how much poetry fills him up as food would when we like a certain food we keep eating it over and
over again because we like the way it taste when he mentioned the ink is pouring out his mouth is explaining how juicy it is to him and makes him want to get more in more into it he’s using figurative speech at that point.