Add Support for Watching a Process for Compiler Errors

Many programming languages and development workflows provide processes that continuously watch for changes and compile code (e.g., npm run watch in JavaScript/TypeScript, cargo watch in Rust, or similar equivalents in other ecosystems). I’d like to request a feature to integrate a "watch mode" into claude-code that monitors a process and reports compiler errors in real-time as changes are made.

This would improve the developer experience by providing immediate feedback on syntax errors, type issues, or other compilation failures without requiring manual re-runs of the build process (which can be expensive in large codebases).