It sounds like the issue is mostly your CarPlay cars small screen compared to Tesla's large one. This didn't seen to be a CarPlay problem beyond maybr Apple trying their best with the screens most of their customers are given.

I believe iOS 27 brings a MiniPlayer, but I don’t know the rules about when it does/doesn’t show.

Would this not be an issue with any interface if the screen is that small?

I mean, you choosing not to use the feature doesn't mean the feature doesn't exist and fulfill your needs.