Admin APIs should fail when we identify that the file system is incorrect

This came from an internal investigation. Customer tries to do an "Export template" and was expecting list of functions to be populated. This normally works, but in this scenario, the following was happening

- There were file system failures. Therefore the host was in the process of shutting down (as mentioned in #5151). Which is by design.
- However, just before host completes shutting down, syncTrigger operation happens resulting in an empty list of functions. (Maybe all /admin APIs should fail when the host is in the process of shutting down?)
- ARM API call will now return this cached information above when it tries to get a list of functions thus leading to an empty function list.

Requires further investigation . @mathewc

Start by tracing the syncTrigger operation and the admin APIs during the host shutdown path described in #5151, then compare that behavior with the ARM request that reads the cached function list. Determine where file-system failure is identified and verify that the affected admin API no longer returns an empty list while shutdown is in progress.

Written by the indexing model from the issue text.