The small library you want is likely the standard (or popular) logging library in your language/framework. For example in Node.js that might be Pino or Winston.

The automatic instrumentation part is for tracing, which arguably is a _huge_ value add on top of logging, but is indeed more complicated to get setup.

Unfortunately I think OpenTelemetry doesn't do a great job in expressing the different parts of the project and how they all fit together (though this is the status quo in observability in general). I think third party vendor documentation tend to do a better job in explaining how to get started with it without needing to piece together the exporters, batchers, context managers, etc.

Disclaimer: I'm building hyperdx, an otel-based OSS observability tool, so I'm pretty biased in being pro-OpenTelemetry :)