Hello @Maxwell, usually there is a charge to whatever payment method you used. This would be one way to see if your purchase of cyberpunk 2077 has gone through. From the phone Stadia app, head into your account settings by pressing your avatar icon on the upper right corner -> press Purchases & subscription -> search your Transaction history to confirm your game purchase.
If you know that a charge as gone through or found the purchase inside the Stadia phone app, I would recommend the steps that @AndroiFy stated. Perhaps accessing Stadia from a different device might help.
---
Please mark posts that helped you to solve your problem as an "Answer" or give "Kudos" to other helpful posts.
