Let us define an observable microservice as one that exposes its internal state through events, metrics, and trace data. Ideally we can aggregate this data in some sort of centralized observability system for alerting and diagnostics. In my opinion there are tools that work much better than others and I will use those in this example but the most important part is that you have a starting point and your services can be observed and alerted on somehow. If your company does not have the means to setup all of this infrastructure you should consider buying one of the many SaaS options out today.
Disclaimer: I am not a native .net or F# developer, I think at this point in my career I've logged 2 weeks on an F# dev team so the implementations given below may not be idiomatic, however, my experience comes from being apart of both Devops and microservices dev teams in other teams and organizations.
That being said; let's start building an "observable" micro