Implement nvm as a standalone binary

[virtualzx-nad]

Original issue from nvm-sh/nvm nvm-sh#3257

Implement nvm as a compiled binary instead of shell scripts to improve performance and reliability.

Required features:

1. Core functionality:
   • Version management
   • Installation/uninstallation
   • Version switching
   • Alias management
2. Shell integration
3. Cross-platform support
4. Migration path from script version
5. Performance improvements
6. Comprehensive testing

Technical considerations:

• Choice of implementation language (Go/Rust)
• Binary distribution
• Shell completion
• Environment management
• Backward compatibility

This is an advanced task that requires:

• Systems programming experience
• Understanding of shell integration
• Cross-platform development
• Performance optimization