Thanks for posting this question in Q&A.
As per the nuget package's documentation, HealthChecks packages does not include Azure functions and app services. However, Azure functions provides out of the box healthcheck feature that you can utilize. Please note that, this feature is only available for functions running on dedicated app service plan and Elastic premium plan.
Healthcheck feature: https://learn.microsoft.com/en-us/azure/app-service/monitor-instances-health-check
I hope this helps!
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