1/2
Based on my understanding of your issue description, it seems like you are experiencing slow SqlConnection.Open or OpenAsync() method with Azure App Service and Azure SQL Database periodically and have tried some steps to isolate the issue.
To narrow-down the issue further, there could be several reasons for this issue.
1.One of the reasons could be that you are hitting the limit while making new outbound connections. The limits you can hit include TCP Connections, which is associated with the size of the worker used. Each instance on Azure App service is initially given a pre-allocated number of 128 SNAT ports.
The SNAT port limit affects opening connections to the same address and port combination.
2.If your app creates connections to a mix of address and port combinations, you will not use up your SNAT ports. The SNAT ports are used up when you have repeated calls to the same address and port combination. Once a port has been released, the port is available for reuse as needed. The Azure Network load balancer reclaims SNAT port from closed connections only after waiting for 4 minutes.
As outlined in this doc section #2-collect-data / review the logs to fetch more info.
App Service provides diagnostic functionality for logging information from both the web server and the web application.
Reference:
Troubleshooting intermittent outbound connection errors in Azure App Service