Is there a good way to share configuration between apps in Azure?
One way would be to use the new App Configuration service: https://docs.microsoft.com/en-us/azure/azure-app-configuration/overview.
It is meant for sharing configuration settings across components.
Note it is not meant for secrets, that's what Key Vault is for.
Best Practice in Architecture: You can use the external configuration store pattern and use a Redis Cache to share the configuration between multiple applications as described in here: https://docs.microsoft.com/en-us/azure/architecture/patterns/external-configuration-store
The approach is you can get this data from Appsettings for each environement (this can be automated in CI/CD pipeline). On first connection you store the data in RedisCache.
For senstive data: Use Keyvault to store the secrets/keys/certificates.