That's right, you're going to want to back up your old iPhone after you have your new iPhone 13 in hand, so the backup is as up-to-date as it can possibly be.
While you wait for backups and updates, check out our guide to iOS 15 to get up to speed with the latest iPhone operating system. Sure, it seems like an unnecessary drag, but this stuff is going to really save you a lot of time and frustration later. We have a little setup advice you're going to want to heed.