I would say that the ZDX is not officially supported with the SuperCharger network. You CAN use it however but you kinda have to cheat. I've done it.
I have an A2ZEV Typhoon Pro adapter. Get the Tesla app, create an account, and attach a credit card to it for billing. Identify your car as a Lyric however, and that you have an adapter. Now, go to any Supercharger that the Tesla app says the Lyric can use. Initiate a charge from the app. When the app tells you to, insert the adapter and cable onto the ZDX charging port. It will start charging.
It's frustrating for sure, especially since the built-in navigation system will not route us to SuperChargers yet. But in a pinch it works.
This is ridiculous. GM has had access since mid September. Why it takes non-GM Ultium-based cars this long is not justifiable.