Thank you for getting back.
Not sure if you tried the PowerShell method mentioned in my comment above or else tried adding the App service using its FQDN or its IP address. As documented here for App Gateway the backend pools can be across clusters, across datacenters, or outside Azure, as long as there's IP connectivity.If you are able to add the app service as backend pool member using its FQDN or its IP address then this is a Portal issue and as we were unable to reproduce the issue on our end, a support request will be required to resolve this issue. It will help if you could file support request for this issue and also share the browser trace with the support engineer to help troubleshoot this issue. Please let me know if you need any help in creating the support request.
If you are unable to add the app service as backend pool member using its FQDN or its IP address then please share the error observed as it will help further troubleshoot this issue.
Hope this helps! Please let me know if you have any additional questions. Thank you!