I can't download iOS 16 from iPad settings

Unlike iOS16 for iPhone, released yesterday, iPadOS16 is not due for release until sometime in October. 

However, iPadOS 15.7 was also released yesterday - incorporating essential security updates.

About the security content of iOS 15.7 and iPadOS 15.7 - Apple Support

While iOS16 is available for iPhone, iPhone owners have the option to just install iOS15.7 at this time.

iPadOS 16 coming sometime in October 2022.

Tap this link below.

iPadOS 16 Preview - Apple

The regular release for iPadOS 16 will not be until October.

As long as you’re OK with having a beta, it’s perfectly all right.

iOS 16 won't be available for iPads until sometime in Oct. At that time, you will need to uninstall the beta version before you can get the solid version.