The new Siri UX needs improvement and to match the UX of talking to chatGPT. At least in settings have an option to keep the Siri window always on top (just have a prominent X out to go to the screen below) and always listening ready to continue your conversation like the experience is with chatGPT.
Been running the beta since June -- on the latest beta now and 8 out of ten times to continue the conversation with Siri (most notably in the car with my phone docked) I have to constantly say "Hey Siri."
One thing it's current UX has over chatGPT voice tech as it shows you the text and provides visuals while chatGPT's UI shows no text and or visuals.