chore: Clean up obsolete files and add Puppeteer chat test

- Remove obsolete documentation, examples, and utility scripts
- Remove temporary screenshots and test files from root
- Add test_chat_backend.js for Puppeteer testing of chat RAG
- Update .gitignore

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.gitignore

@@ -43,6 +43,8 @@ stream_extract.py
 quick_vectorize.py
 vectorize_remaining.py
 migrate_chunk_*.py
+!generations/library_rag/migrate_chunk_v2_to_none_vectorizer.py
+!generations/library_rag/fix_turings_machines.py
 
 # Archives (migration scripts moved here)
 archive/chunk_v2_backup.json