After working with support to confirm my problem I believe I've found a solution. Thank you @GitaraniSharma-MSFT for answering this questions about Service Tags. (https://video2.skills-academy.com/en-us/answers/questions/48025/questions-about-service-tags.html)
The Access Restrictions was blocking in bound traffic from the Azure SQL Servers causing time outs and crashing my App API. Adding the SQL gateways IP addresses for the appropriate region did not help because the Web API is situated on the Azure Network and does not need to go through the gateways (different IP external vs internal). I instead add an Access Restriction with type Service Tags https://video2.skills-academy.com/en-us/azure/app-service/app-service-ip-restrictions#set-a-service-tag-based-rule Each service tag represents a list of IP ranges from Azure services. I added AzureCloud is an available Service Tag and it seems to cover ALL Azure products.
Although SQL is a valid Service Tag, SQL was not deemed a common Service Tag and is not available in the drop down. (Perhaps this could be added in the future as it should be fairly common that an Azure Web API communicates with an Azure SQL Server)
Note: You must create a new access restriction and set the type to Service Tag. The Portal does not allow you Edit an existing Access Restriction from one type to another (EG: IPv4 to Service Tag)