I've spent the morning trying to deploy my static storybook to a Azure Static Web App. I've found a few blog posts about it but they seemed a bit outdated.
Finally i figured out that you could just do everything with the AzureStaticWebApp pipeline task.
For me it worked to just add this command to a pipeline.
- task: AzureStaticWebApp@0
app_build_command: 'yarn build-storybook'
You will need to add a $(deployment-token) variable that you will find on your static web app in Azure, but otherwise that was all i needed, no need to run any custom yarn commands and so on.