test(docs): run docs invariants in CI

[hansjm10]

Sequence

Order: 3 of 12
Phase: Phase 1 - Navigation and Freshness
Design: docs/agent-first-workflow-design.md
Tracker: #908
Depends on: #910

Agent Role

Workflow Infrastructure Agent

Scope

• Add a test:ci script to @idle-engine/docs that runs the existing docs invariant test.
• Ensure the root workspace pnpm test:ci runner executes docs invariants.
• Update docs guidance if the docs validation command changes.

Context Packet

• packages/docs/package.json
• packages/docs/scripts/test-docs.mjs
• tools/scripts/run-workspace-script.mjs
• package.json
• .github/workflows/ci.yml
• docs/agent-first-workflow-design.md

Acceptance Criteria

• packages/docs/package.json includes test:ci.
• pnpm --filter @idle-engine/docs test:ci passes.
• A root pnpm test:ci run would include docs tests through normal workspace script discovery.
• No docs build or lint behavior regresses.
• Any docs about validation commands are updated if needed.

Validation

• pnpm --filter @idle-engine/docs test:ci
• pnpm test:ci --filter @idle-engine/docs
• pnpm docs:build

Notes

• Keep this issue narrowly scoped; do not add new doc coverage rules here.

Refs #906