Integrate with logging / tracing framework

For use in productive environments we need to provide basic logging, or maybe even better distributed tracing within the library.

The [Tracing](https://github.com/tokio-rs/tracing) framework by the Tokio team seems to be a popular choice.

No files, tests, or entry points are named. Start by surveying the crate structure and existing dependency configuration, then review how the library performs client operations before deciding whether the requested scope is logging, distributed tracing, or both; done requires an agreed integration approach and corresponding coverage.

Written by the indexing model from the issue text.