Refactor: Create providers package to modularize LLM client implementations

[jxnl]

The current flat structure with individual client_*.py files has become difficult to maintain as we add more providers. We should reorganize into a proper provider package structure.

Current problems:

• Flat directory with many provider-specific files cluttering the root namespace
• Related provider code is scattered across client_*.py and process_response.py
• No clear interface that providers must implement
• Difficult to discover which functionality is supported by which provider

Proposed solution:

instructor/
├── providers/
│   ├── __init__.py     # Provider registry and common utilities
│   ├── base.py         # Provider interface/protocol
│   ├── oai_provider.py # OpenAI implementation (avoid name conflict)
│   ├── claude.py       # Anthropic implementation 
│   └── ...             # Other providers

Each provider module would contain:

1. Factory functions (e.g., from_openai)
2. Provider-specific response handlers (moved from process_response.py)
3. Provider-specific validation logic (mode support, etc.)
4. Provider-specific utility functions
5. Structured comments documenting supported features

Implementation steps:

1. Create providers/ directory with placeholder __init__.py and base.py
2. Move each client_*.py file into corresponding provider module with non-conflicting names
3. Move provider-specific handlers from process_response.py to provider modules
4. Update imports throughout codebase
5. Update type annotations to reflect new structure