### What problem does this PR solve?
Fix:
- Use @ to avoid split by `_` in model_name.
- Verify api_key when add instance.
- Pop api_key in list intances response.
- Remove useless index.
- Sort providers, instances and models by name.
- Get `is_tools` from llm_factories.json
### Type of change
- [x] Bug Fix (non-breaking change which fixes an issue)