What's the difference between B and C? API being down seems like an anomaly.

Also, you can't know how frequently you'll get 500s at the time you're doing integration, so you'll have to go back after some time to revisit log severities. Which doesn't sound optimal.

Exactly. What’s worse is that if you have something like a web service that calls an external API, when that API goes down your log is going to be littered with errors and possibly even tracebacks which is just noise. If you set up a simple “email me on error” kind of service you will get as many emails as there were user requests.

In theory some sort of internal API status tracking thing would be better that has some heuristic of is the API up or down and the error rate. It should warn you when the API is down and when it comes back up. Logging could still show an error or a warning for each request but you don’t need to get an email about each one.