A similar question was asked about monitoring connections to Cosmos db at https://stackoverflow.com/questions/62189308/how-can-i-monitor-the-currently-open-connections-of-an-azure-cosmos-db
It looks like you either have two options (provided by Matias Quaranta)
Azure Monitor has the Connections metrics: https://learn.microsoft.com/en-us/Azure/app-service/web-sites-monitor#understand-metrics
Also, App Service has the Diagnostics Tool that includes Connections: https://azure.github.io/AppService/2018/03/01/Deep-Dive-into-TCP-Connections-in-App-Service-Diagnostics.html
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