Hello AdamSchumph-ETI'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others", I'll repost your solution.
Please click "Accept" the answer as original posters help the community find answers faster by identifying the correct answer.
Issue : I purchased a domain through a Static Web App; but digwebinterface.com doesn't find any DNS records
Resolution : The solution was to find the Azure App Service Domain, not the Azure DNS.
please don’t forget to close the thread by clicking Accept the answer wherever the information provided helps you, as this can be beneficial to other community members.