Refactor sidebar overlay modules

[heznpc]

Summary

• split shadow UI root helpers, PDF export, and chat sub-panel state into focused content modules
• wire new modules into manifest load order and runtime module contract
• update adjacent ownership comments and _sb typedefs

Tests

• npm run lint
• npm run format:check
• npm test -- --runInBand
• npm run build:bundle
• npm run test:e2e
• npx playwright test tests/e2e/pdf-export.spec.js --workers=1 --reporter=line