My iPad Pro 2021 does not show the option to download iOS 16. How can I obtain that update?

Correct. Unlike iOS16 for iPhone, released 12th September, iPadOS16 is not due for release until sometime in October. For reasons known only to Apple, release dates for iOS for iPhone and iPadOS for iPad have been deliberately staggered.

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

When iPadOS16 is released, it will be available for these models of iPad:

• iPad Pro (all models)
• iPad Air (3rd generation and later)
• iPad (5th generation and later)
• iPad mini (5th generation and later)

You can obtain it by waiting until it is released sometime later in October.