Complete documentation cleanup for pure Symbolics.jl

📚 **Documentation Fully Updated:**

## ✅ **All References Fixed:**
- ❌ Removed all SymbolicUtils.jl references from docs
- ✅ Pure Symbolics.jl examples throughout
- ✅ Consistent @variables syntax
- ✅ Updated manual pages and README

## 📋 **Updated Documentation:**
- **index.md**: Pure Symbolics.jl examples, removed dual API
- **README.md**: Showcases arctangent integration
- **manual/**: All examples use @variables and Symbolics
- **docs/Project.toml**: Removed SymbolicUtils dependency

## 🎯 **Clean, Focused Documentation:**
- Single clear API for users
- Modern Symbolics.jl ecosystem integration
- No confusion about which package to use
- Professional presentation

**Documentation ready for pure Symbolics.jl ecosystem!** 📖

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: claude