Add demo API connection banner

[smithaldon1]

Summary

• Add a reusable simulator-backed demo notice across the Workbench shell and loading state.
• Add an Overview API connection banner that shows the configured FastAPI target, health status, and simulator-backed demo source.
• Improve API failure panels with presenter recovery guidance for make demo, make api, and NEXT_PUBLIC_API_BASE_URL.
• Update the Workbench README, demo runbook, tests, and learning log for the new visible behavior.

Closes #176

Test Evidence

• cd apps/web && npm test: 12 passed
• cd apps/web && npm run lint: passed
• cd apps/web && npm run typecheck: passed
• git diff --check: passed
• make lint: passed
• make typecheck: passed
• make docs: passed (Markdown-only docs checker placeholder)
• make test: 195 passed
• make test-e2e: 1 passed
• cd apps/web && npm run build: passed

Docs Impact

• Updated apps/web/README.md with Overview API state and API recovery behavior.
• Updated docs/demo/OPERATIONS_WORKBENCH_DEMO_RUNBOOK.md with the API state and recovery check.
• Updated docs/LEARNING_LOG.md with the learning summary for issue UI: Add simulator-backed demo data notice and API connection banner #176.

Follow-up Work

• None for this issue. Production monitoring, retry/backoff infrastructure, auth, and environment switching remain out of scope.

[smithaldon1]

Reviewed and approved for merge