ENH: standalone execution check of built notebooks

[mmcky]

A lecture can build cleanly and still break for a reader who downloads it. Benefit: match running a lecture standalone.

The gap is the artifact, not kernel isolation — jupyter-cache already isolates kernels per notebook (single_nb_execution). Download/Colab notebooks come from sphinx-tojupyter (containers/quantecon-build/environment.yml:67) via the jupyter builder (build-lectures/action.yml:104, output :126, staged to _build/html/_notebooks :71-76), and nothing here executes them, so conversion defects ship silently. Scope is executing them (PLAN.md:117); both options first floated are dated — a venv off a base anaconda image fights the pinned-as-a-set policy (PLAN.md:96-102), and the preferred jupyter-book/MyST-NB/myst-parser engine runners were never pursued upstream.

Work items

• Weekly cache workflow (templates/cache.yml:22, 0 0 * * 0): execute each _build/jupyter/**.ipynb in the pinned container, report per-lecture pass/fail
• Ensure notebooks exist: jupyter builds only when requested (build-jupyter-cache/action.yml:162, built :160-166) and the template ships builders: 'html' with jupyter commented (templates/cache.yml:73-75), so require jupyter or build them
• Settle the runtime budget for re-executing every lecture weekly; may depend on Optimize preview builds: phased plan for the fastest PR previews (tracking) #92 Phase 3's parallel pre-execution
• Decide whether failure blocks the cache save or only reports
• Alerting: build-jupyter-cache's failure-issue path is inline actions/github-script (build-jupyter-cache/action.yml:382-528), so a new job must extract or duplicate it
• Resolve the "first step of ENH: standalone execution check of built notebooks #2" conflict: Optimize preview builds: phased plan for the fastest PR previews (tracking) #92 Phase 3 and PROJECT-OPTIMIZE-PREVIEWS.md:93 both claim it for the jcache project execute --executor local-parallel pilot — a wall-clock optimisation, not an artifact check. Proposal: Optimize preview builds: phased plan for the fastest PR previews (tracking) #92 drops the lineage, this issue keeps the notebook check.