Improve observability of recompilation checking

There should be a way to get verbose information about recompilation checking, to make it easier to figure out what is causing unnecessary recompilation.

Two ideas:

- Some `Verbosity`-related mechanism that allows one to quickly get a dump of ALL the information related to recompilation checking, not interleaved with anything else.
- Provide a way to report exactly what changed when a monitored value changes (e.g. as a small diff). This would require reworking the `FileMonitor` machinery a little bit so that we can provide diffs when values change.

The issue names no files or tests; start by locating the recompilation-checking entry points and the FileMonitor machinery. Compare the proposed Verbosity-related dump with reporting diffs when monitored values change, then define which approach is accepted and how its output should be verified.

Written by the indexing model from the issue text.