Mysterio learned that EDITH was under the possession of Nick Fury, but of course, Fury keeps things very under wraps, so he needed a plan to gain his trust. Mysterio would help Fury's team detect new elemental threats, and Hydro-Man was going to happen in Venice. Peter Parker's school trip might have been entirely orchestrated by Fury to coincide with elemental threats even since the beginning to allow Peter to be in Venice when the elemental attack occurs. Quentin Beck was probably informed about who Spider-Man was, because Fury saw Mysterio as a hero to trust on, and all of the Avengers know who Spider-Man is, so no biggie. Quentin would then deduce that Fury wants to give EDITH to Peter Parker, and that's when he begins to spy on him, in Venice, in anticipation of Hydro-Man's attack.
This would be my best reflection on how it all went down.
