My iPad Pro doesn’t show iOS 16 available for download

Correct. Unlike iOS16 for iPhone, released 12th September, iPadOS16 is not due for release until sometime in October. 

However, iPadOS 15.7 was also released 12th September - 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.

More information about the forthcoming iPadOS16 can be found here:

iPadOS 16 Preview - Apple

iPad OS 16 has not been released.

Apple states it will be ready in October.

Yep, their both right. iOS 16 is out, but iPadOS 16 will have to wait till October, hopefully. I’ve also heard stage manager will only will be available on M1 iPads too.