You've plenty of pigeons and in my neck of the woods, we have a very similar bird that is in the same family, Mourning doves.
While pigeons are very brazen, mourning doves are very skittish, taking flight at the drop of a dime.
'at the drop of a dime' - I like this wording, sounds a nice vocabulary!
this summer my family is at our summer place, and one morning my wife witnessed a wild representative of this family, wild forest pigeon; it was size of a duck, but shy and skittish exactly like a Mourning dove you mentioned - it took off in a moment when noticed her at 15m distance... she had no time to take any photo 🙃
!PIZZA