Include public examples in the standard verification story

[lbliii]

Context

Examples are public teaching material and many have their own tests, but the standard pytest config only collects tests/. That means example-specific tests can silently rot unless someone remembers to run them manually.

Evidence

• pyproject.toml sets testpaths = ["tests"].
• find examples -maxdepth 2 -type f -name 'test_*.py' | wc -l reports 26 example test files.
• tests/test_examples.py only smoke-runs a curated list of run.py examples and explicitly says output correctness is not checked.
• Many app.py examples have colocated tests under examples/*/test_*.py that are outside make test and make test-cov.

Proposed Scope

• Add a make test-examples target and decide whether it belongs in verify-stability.
• Update CI to run example tests, or move example tests into tests/examples/ if that is the intended collection model.
• Keep optional-dependency examples isolated with skips/importorskip where needed.

Done When

• Example tests run in an explicit documented gate.
• New examples have a clear testing convention.
• examples/README.md, tests/test_examples.py, and CI agree on what is runnable.