I don’t have stage manager on my iPad Pro 11

Per Apple.

iPadOS 16 coming sometime in October 2022.

Tap this link below.

iPadOS 16 Preview - Apple

Also, you need an iPad Pro with an Apple M1 CPU to have the Stage Manager feature as part of iPadOS 16.

Stage Manager is an element of the forthcoming iPadOS16. Unlike iOS16 for iPhone, released 12th September (iOS 16.0.1 subsequently released 16th 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.

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)

More information about the forthcoming iPadOS16 can be found here:

iPadOS 16 Preview - Apple

Since iPadOS 16 has not yet been released there’s no way for you to have it.

Do you have an iPad Pro with an M1 processor?