Hi Michael W,
Make sure that your azure is required in the deployment tokens used in the static static web app. You may need to set a deployment authority policy to use an azure deployment token, which is recommended for better protection.
Make sure that your azure account has the required roles to reach the repository. The roles that generally required the required permissions include the owner, contributor or website contributor. If you do not have these roles in your account, then you have to work with your Azure administrator to play the appropriate role.
If you are using Yaml pipelines, consider enabling access to repository in the settings of YAML pipelines. This setting requires clear permission to access all Azure representative repository, which can help resolve issues of permission.
check the repository is not set in private until you have configured the permissions required for the deployment tokens to access it.
https://learn.microsoft.com/en-us/azure/devops/pipelines/security/secure-access-to-repos?view=azure-devops&tabs=yaml#build-pipelines
https://learn.microsoft.com/en-us/azure/app-service/deploy-continuous-deployment?tabs=github%2Cgithubactions#frequently-asked-questions
https://learn.microsoft.com/en-us/azure/static-web-apps/build-configuration?tabs=identity&pivots=github-actions#file-name-and-location
If the answer is helpful, please click Accept Answer and kindly upvote it so that other people who faces similar issue may get benefitted from it.
Let me know if you have any further Queries.