Rework the logging to distinguish "skipping updates" from "already updated"

[favonia]

The current logging is confusing because it does not distinguish cached API results from genuine ones. It means the user might think the tool is performing real checking and updating while it's just using cached results. Inspired by the discussions in #680.

This enhancement requires slight adjustments to the internal API to expose whether the result is cached or not.

Maybe some documentation changes, too.