Chase Goebel, thank you for providing additional details about this issue.
I tested the bicep code shared above and it worked fine for me. This issue seems to be related to absence of resource group in subscription or you do not have access to a resource group to which you can deploy bicep file. Ensure that a resource group is already created and available in Azure Portal. RG creation during the bicep deployment process does not work. Even when you do bicep deploy using CLI, a resource group is created first Deployment scope. For more details, see https://learn.microsoft.com/en-us/answers/questions/1431322/how-to-resolve-azure-static-web-(extension)-error
In case the steps above do not help, I would suggest reaching out to Azure Support as it will require 1:1 troubleshooting with access to logs and machine to understand the root cause.
Hope this helps.
If the answer helped, please click Accept answer so that it can help others in the community looking for help on similar topics.