Dragonfly sounds most likely. You don’t get cicadas do you ? They are very large. Maybe one came over from my side of the world. They are very loud in Summer.
There are millions of insects so without a description will be impossible to say. There was a large insect on the inside of my kitchen window the other day with a head like a hammerhead shark and a stick like body, I think a type of moth.
looking out the window this morning I saw a large insect flying about, it was about an inch and a half long, didn't land anywhere, just kept flying up and down, it wasn't a bee or wasp or butterfly,OH couldn't see it , it was so clear against the blue sky, but he still couldn't see it it wasn't brightly coloured so it was probably brownish.