Syncing with iCloud (messages)

So I got a new iPhone and I transferred everything from my old iPhone to my new phone. In my messages app it says “syncing with iCloud” does this mean that I will get back all of my old messages? Do I have to keep the message app open on my screen in order for the syncing to complete or can I just leave it open in the background and the syncing will complete? I’m mainly concerned if I’m going to get all of my old messages back. I had plenty of storage on my old phone and got more storage on my new phone so I’m hoping that my messages will transfer over eventually. Thank you in advance for the help!!!