Twitch makes it easy to push a button to do reruns. Not sure they care to delete the extra time as it would just cost time/money. Sure wish Twitch could automatically remove the pause screen for reruns!
I tried out Streamlabs which seems to be the streaming platform of choice for Twitch and others. You can have a waiting to start screen/pause/whatever while you connect to the streaming platform but are still getting things ready in the other window. My understanding of the workflow is you start your Twitch stream via Streamlabs which then shows the waiting to start screen(or anything you want to show), start your video chat program which involves sometimes restarting connections and making sure mikes work etc, load up your other content you want to show on the stream, arrange all the windows in streamlabs, then press start stream. Some content creators have a different workflow, but with all the pictures and stuff GW's stream shows it sounds like they have a 3rd person doing the stream and they just connect via a video chat like Zoom.