You can test the server's connection to an Azure SignalR Service using Azure Functions for example:
https://learn.microsoft.com/en-us/azure/azure-functions/functions-bindings-signalr-service
About the connectivity:
When the app server starts, in the background, the Azure SDK starts to
initiate server connections to the remote Azure SignalR. As described
in Internals of Azure SignalR Service, Azure SignalR routes incoming
client traffics to these server connections. Once a server connection
is dropped, all the client connections it serves will be closed too.
As the connections between the app server and SignalR Service are
persistent connections, they may experience network connectivity
issues. In the Server SDK, we have Always Reconnect strategy to server
connections. As the best practice, we also encourage users to add
continuous reconnect logic to the clients with a random delay time to
avoid massive simultaneous requests to the server.
https://github.com/Azure/azure-signalr/blob/dev/docs/tsg.md#server-connection-drop