[qorud02]

Both metadata cacher examples currently fail when copied and executed: the automatic-stage example calls geet_path() during saving, and both examples save the_best_number but read best_number during loading.

Use the existing get_path() method and the same metadata key in save/load. Add tests that extract and execute the actual documentation code blocks rather than maintaining separate copies. One test runs the real stage decorator through saving and a cache hit; the other checks explicit inline metadata saving/loading.

Before the documentation correction, the two tests fail with AttributeError and KeyError. After it, both pass. Black, isort, flake8, and git diff --check passed. The repository-wide suite and full documentation site were not run for this change.

This contribution was developed with AI assistance and verified against the real cache implementations.