I'm having the same issue on iPhone 15 Pro Max, from iOS27 beta 1 through 5. It's been weeks and my phone has been connected to Wi-Fi, has plenty of storage space, and the system and Siri languages match. The same configuration works on my iPad.
I tried turning Siri off and on, reverting to old Siri and back to the beta, restarting my device and updating iOS.
It just says 'Adding support for Siri is in progress'.
I don't have the new Siri app and typing 'siri://' in Safari tells me to download it from the App Store, where it's not available.
I submitted a report in the Feedback app during the previous beta.
Topic:
Machine Learning & AI
SubTopic:
Apple Intelligence