Hi anonymous user,
Multi-container support where a container is being used in a sidecar manner as you are doing is only available on Linux containers, not Windows. If your app service is being hosted in Windows container, please switch it over to Linux. See https://azure.microsoft.com/en-us/blog/app-service-adding-multi-container-capabilities-and-linux-support-for-app-service-environment/ for more information. Even though this blog post references using a Linux ASE, you should be fine with using an app service.
I also noticed you posted the docker-compose on your stackoverflow question as well. If you are hosting your app inside a Linux app service, please let me know as this may be signs of an issue.
Regards,
Ryan