You can set budget alerts, this article explains how to do so. Setting up a budget alert will not prevent “overage” charges. They are more like a notice that you are going to be charged. I think you could set a $200 budget (or less) and when you receive the notification, you could disable the API key manually in the Google API Console so you will not get charged. But, then you will not have maps and the error you see now will be displayed instead.
Please keep in mind, using the Google Maps Platform APIs was never free, there were quota limits. When you reached that limit, Google would no longer serve maps to your site. Because the quota limit was generous most sites under normal usage would never hit the quota limit.
Google now requires a valid billing address and payment method so they can bill as you utilize their platform. They dub this “Pay as you go”. The recurring $200 credit on your billing account is roughly equivalent to the to the previous free quota limits in terms of usage of their platform.
All this said, unfortunately you only have two options. Set up billing with Google or disable the display of maps.
I hope this helps, let me know!
ps. I am working to add multiple map service provider support in Connections. There are free providers, but they are slow compared to Google and the geocoding (process of converting an address to a pin on a map) accuracy is not the greatest. The multiple map service provider support in Connections will default to the free providers. This will require updates to all templates after this support is fully implemented. In addition to the free providers, there will be support for commercial providers such as Google and Bing. So, at least this way you will be able to choose your poison, so to speak.