Prevent new work while Job Host is shutting down from adding `app_offline.htm`

The biggest case where we have seen issues with this is a non-packaged deploy, where a deployment adds app_offline.htm but also immediately starts to signal Job Host restarts from making file changes.

Example of an error caused by this: https://github.com/Azure/azure-functions-host/issues/4328

No file or test is identified in the issue. Start by tracing Job Host shutdown and restart signaling alongside the non-packaged deployment path that adds app_offline.htm; done means new work cannot add app_offline.htm during shutdown and the error described in issue 4328 no longer occurs.

Written by the indexing model from the issue text.