It's only been 11 days since Apple released iOS 13, and the OS is getting its third update today. In fact, you might recall that iOS 13.1 was originally supposed to launch today, but that release date was bumped up by six days amid complaints about iOS 13. Since then, there have been two bug fix updates, the second of which is out today.
iOS 13.1.2 and iPadOS 13.1.2 actually contain some notable fixes though. There was an issue with iCloud backups where the progress bar would still show, even after it's done. Apple also fixed an issue that caused the Camera app to not work properly, and there's a similar fix for the Flashlight.
Other fixes include Bluetooth connectivity in vehicles, an issue where shortcuts wouldn't work on HomePods, and an issue that caused the loss of display calibration data.
If you've got an Apple Watch, there's a bug fix update for that, which is watchOS 6.0.1. That update fixes an issue with the Mickey and Minnie Mouse watch faces, an issue where the Calendar complication might not show you upcoming events, and an issue that causes the loss of display calibration data.
As far as new features go, there aren't any. You'll have to wait for the next minor updates for that, and watchOS 6.1 is already in beta. Apple will likely seed iOS 13.2 betas sooner rather than later, possibly sometime this week, since iOS 13.1 originally wasn't supposed to launch until today anyway.