Why does the background picture on my homepage disappear and become a black background for my apps on iPhone 13?

Hello bevjerry,

Thank you for reaching out to Apple Support Communities.

Let's set up your wallpaper again using the same photo. These steps should guide you:

"Add a new wallpaper for your Lock Screen or Home Screen

1. In the Settings app, tap Wallpaper.
2. Tap Add New Wallpaper.
3. Tap Photos, People, or Photo Shuffle to choose your own photo. You can also select a wallpaper from a category like Weather & Astronomy, Emoji, Collections, or Color.
4. If you want, you can customize your wallpaper further. Then tap Add.
5. Tap Set as Wallpaper Pair and your selection will be seen on both the Home Screen and Lock Screen. Tap Customize Home Screen to create a separate Home Screen wallpaper that you can edit."

Additional details can be found here: Change the wallpaper on your iPhone

If the issue persists, can you provide a few more details? Does the same thing happen if you choose another photo? Also, which iOS version do you have installed?

Cheers!