Drain mode is not initiated when terminating a Functionapp in Kubernetes

#### Investigative information

When I ran my Functionapp in a Kubernetes cluster, I observed that the Functionapp initiates drain mode and unregisters all the listeners from my application when I delete a Kubernetes pod or scale in my Kubernetes deployment.


However, when I upgraded my Functionapp to use the Azure Functions V4 runtime, I noticed the Functionapp no longer initiates drain mode as before - subsequent messages put into the queues continued to trigger the functions.


#### Expected behavior

* Functionapp initiates drain mode and unregisters all the listeners from the application when a Kubernetes pod termination occurs.

#### Actual behavior

* Functionapp continues to execute to handle incoming triggers.

#### Related information

The above can be reproduced in a personal sample project I have created here:
- [Sample codes for containerized functionapp on v4 runtime](https://gitlab.com/victorchuack/adf-playground/-/tree/containerization-v4)
- [Sample codes for containerized functionapp on v3 runtime](https://gitlab.com/victorchuack/adf-playground/-/tree/containerization-v3)
Note: The only changes are in the Dockerfile and the csproj, as shown in the [diffs here](https://gitlab.com/victorchuack/adf-playground/-/compare/containerization-v3...containerization-v4?from_project_id=32222648&straight=true)

Start by reproducing the behavior with the linked containerized Function App samples, comparing the v3 and v4 branches and their Dockerfiles and project files. Investigate the host's Kubernetes pod-termination path and verify that deleting or scaling in a pod initiates drain mode, unregisters listeners, and stops subsequent queue-triggered executions.

Written by the indexing model from the issue text.