How long does the iOS 16 update take to install?

Depends on the speed of your Wi-Fi connection and how busy things are with millions of users trying to update at the same time.

Took about 1 hour on one iPhone here and a bit less on another on a 500 Mbps Internet connection.

Once you start the download, you can go back to what you were doing until the iPhone restarts to install the update.

It depends on a lot of factors, including the quality of your Internet connection, and the demand on Apple servers (which is high right now, since the update was just released and everyone is trying to download at once).

No, you do not need to stay in Settings while it is downloading.