refactor(coding-agent): restructured web search and config systems with class-based architecture and type generalization

- Renamed web search types and functions to remove 'Web' prefix for broader applicability (WebSearchProvider -> SearchProviderId, WebSearchResponse -> SearchResponse, WebSearchTool -> SearchTool, etc.).
- Refactored web search provider system from object-based configuration to class-based architecture with abstract SearchProvider base class and concrete provider implementations.
- Refactored ModelRegistry to use direct constructor instantiation instead of discoverModels() helper function, simplifying model discovery pattern.
- Refactored config system to use new ConfigFile class with schema validation, caching, and multi-format support (JSON, JSONC, YAML).
- Simplified Exa API key discovery to check environment variables only, removing .env file reading logic.

packages/coding-agent/DEVELOPMENT.md

@@ -316,7 +316,7 @@ src/
     │   ├── utils.ts          # Scraper utilities
     │   └── (domain-specific scrapers)
     └── search/               # Web search
-        ├── index.ts          # WebSearchTool exports
+        ├── index.ts          # SearchTool exports
         ├── auth.ts           # Search auth
         ├── render.ts         # Search result rendering
         └── providers/        # Search providers