Add Claude API support and fix CORS issues

- Add Claude API integration to LLM service
- Create Express backend server with CORS support
- Add API proxy example page
- Fix CORS errors by routing through backend
- Update LLM configuration to support Claude
- Add package.json with dependencies

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

.claude/settings.local.json

@@ -6,7 +6,8 @@
       "Bash(git config:*)",
       "Bash(git add:*)",
       "Bash(git commit:*)",
-      "Bash(git push:*)"
+      "Bash(git push:*)",
+      "Bash(curl:*)"
     ],
     "deny": [],
     "ask": []