@SvenGlöckner yes it is possible to connect your app service to on prem with Hybrid Connection Manager. Within App Service, Hybrid Connections can be used to access application resources in any network that can make outbound calls to Azure over port 443.
This Azure Documentations shows how to connect on prem to app service [[https://learn.microsoft.com/en-us/azure/app-service/app-service-hybrid-connections#hybrid-connection-manager] and I have also shared the steps below as well:
"After installing HCM, you can run HybridConnectionManagerUi.exe to use the UI for the tool. This file is in the Hybrid Connection Manager installation directory. In Windows 10, you can also just search for Hybrid Connection Manager UI in your search box.

When you start the HCM UI, the first thing you see is a table that lists all the Hybrid Connections that are configured with this instance of the HCM. If you want to make any changes, first authenticate with Azure.
To add one or more Hybrid Connections to your HCM:
- Start the HCM UI.
- Select Add a new Hybrid Connection.

- Sign in with your Azure account to get your Hybrid Connections available with your subscriptions. The HCM doesn't continue to use your Azure account beyond that.
- Choose a subscription.
- Select the Hybrid Connections that you want the HCM to relay.

- Select Save.
You can now see the Hybrid Connections you added. You can also select the configured Hybrid Connection to see details.

To support the Hybrid Connections it's configured with, HCM requires:
- TCP access to Azure over port 443.
- TCP access to the Hybrid Connection endpoint.
- The ability to do DNS look-ups on the endpoint host and the Service Bus namespace. In other words, the hostname in the Azure relay connection should be resolvable from the machine hosting the HCM.
Note
Azure Relay relies on Web Sockets for connectivity. This capability is only available on Windows Server 2012 or later. Because of that, HCM is not supported on anything earlier than Windows Server 2012."
Hope that helps. let us know if you have further questions
Best,
Grace