@howley Thank you for reaching out to Microsoft Q&A.
I understand that you are trying to place the app services in a VNET. And you wanted to know about the reachability and connectivity to the associated services.
For connecting the app service to the VNET, you can try VNET Integration. https://learn.microsoft.com/en-us/azure/app-service/web-sites-integrate-with-vnet
For the dependencies/ related question, please check this: you can use service endpoints. https://learn.microsoft.com/en-us/azure/app-service/environment/network-info#service-endpoints
Hope this answers your question. Please let me know if you are having any questions.