fix(parser): export and variable mappings for graceful fallbacks

feat: complete backend engine logic (llm parsing, puppeteer renderer, sqlite analytics)

fix: force dynamic rendering for api routes using request.url

fix: resolve TypeScript and test configuration issues for Phase 13

feat: integrate insights recommendations and badge into create flow

feat: inject insights into structure API for carousel guidance

feat: add /api/analytics/insights endpoint for carousel creation recommendations

feat: add /api/schedule endpoints (CRUD)

feat: create /api/publish route