How can a CarPlay voice-based conversational app let the car show and control an active conversation?

We make Alchemy, a leadership coaching app on the App Store. In Alchemy hands-free mode, a person talks with their coach out loud. It is a live, two-way voice conversation over the internet, started from a button in the app. Many of our users do this while out for a walk and especially while driving. Here is how it looks on Audroid Auto :

We have requested the CarPlay voice-based conversation entitlement (com.apple.developer.carplay-voice-based-conversation) and plan to build the CarPlay screen with CPVoiceControlTemplate.

Question: for an app with this entitlement, what is the supported way to let the car know that a conversation is active, so that the car can show it on its own displays (for example a name or title in the instrument cluster) and the driver can pause or end it with the steering wheel controls?

What we want. On an Android phone connected to the same car (an Audi with a digital instrument cluster), our voice conversation appears in the cluster's header as an active call with a name, and the steering wheel button ends it. We would like the same for iPhone users, using the APIs Apple intends.

What we tried. iPhone 13, iOS 27.2 beta, wired CarPlay, same car:

1. We started the conversation as an outgoing CallKit call (CXStartCallAction, generic handle, localizedCallerName set), with the audio background modes. The phone showed a call. The instrument cluster did not change, and the CarPlay Phone screen showed nothing.
2. With the audio background mode only, the conversation works well through the car speakers and microphone, on the Home Screen and with the phone locked. The instrument cluster stays on the radio station, and CarPlay shows only the orange microphone indicator.

If the car's own displays cannot show a voice-based conversational app's session, that is a useful answer too. In that case, what can the Voice Control template show the driver, and can the steering wheel controls act on the conversation at all? The goal is truly hands free so nobody gets a ticket while getting coaching help. 👍

Thank you.