You actually dont need the site extension for asp.net core. Just the appsettings and the libraries injected at startup. If you're referring to the APM, that's different though.

My experience is that if I don't add that site extension, it doesn't capture the log messages from my custom code. It does capture some standard logging, but none of the log messages from my code. What is APM?

Application Performance Monitoring is essentially an agent that looks at the runtime and generates performance data for it. For custom code, as long as you're registering the application insights instance as

services.AddApplicationInsights()

etc. and you have the InstrumentationKey for Application Insights as an AppSetting, it should work fine.

OK. Thanks. I'll look more into that. I'm not sure about that instrumentation key.