my Apple iPhone 16 Pro Max says Siri, not Siri and Apple Intelligence

Apple Intelligence has not been released yet.

There is also no support provided when using Beta Software. You are just a bug tester with the only option to report the bugs you find using Feedback. Some things simply won't work in beta software, so it is never recommended to install on a primary device.

Just be patient and let others struggle with any problems.

Some people are running the iOS 18.1 beta. You can get it if you wish, but unless you have a spare iPhone you can use, I'd recommend against running any beta.

Regards.