Azure Function to SignalR (Serverless) to Web app

What's the role of your Azure Function? Do you still have Hub logics defined in your Web Apps?

When in Default mode, your Web App handles the lifetime of the clients, the SignalR service acts like a proxy that it routes all the client traffics through server connections to the Web App, while in Serverless mode, the SignalR service handles the lifetime of the clients. This article describes the differences in detail.

If you still have your Web App handle the clients in the Hub class, and Azure Function is simply used to send messages to these clients, please use Default mode.