[HealthChecks] Add Diagnostic HealthChecks

[jviau]

Health Checks Today

Customers on dedicated/premium function apps can configure a health check today. This is an HTTP endpoint which the platform will poll to determine instance health. This work will not replace that but potentially augment it. The health checks today are purely customer implemented, only offering health for the customer side of the instance. This work will add platform / functions host health. Customer's will have the option to incorporate this health check with their own.

Proposal

To improve observability of a functions app, we should incorporate a robust health checks system in the functions host. This will give immediately feedback on the general health of a function app and can be incorporated into liveness probes as necessary (e.g. #9181).

Steps

1. Adopt Microsoft.Extensions.Diagnostics.HealthChecks package.
2. Design and implement select health checks for different areas.
3. Expose a health check endpoint.
4. Publish health check results to telemetry.

Will expand on this issue at a later date with more details and a breakdown into sub-tasks.