Hi, Izzyvan!
Thanks for visiting the Apple Support Communities. If I understand your post, you're having trouble accessing the Battery widget on your iPad Air. When you try to add it from the Today screen > Edit, it just doesn't appear in the list. I'm happy to help!
First, force close the Settings app on your iPhone, and any other open apps: How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support, then restart your phone: Restart your iPhone, iPad, or iPod touch - Apple Support.
If the issue continues after that, I would recommend backing your iPhone up: How to back up your iPhone, iPad, and iPod touch - Apple Support, then using the steps under the "Reinstall iOS" section of If you see the Connect to iTunes screen on your iPhone, iPad, or iPod touch - Apple Support to reinstall the iOS software.
Have a great day!