🧹 Refactor execute function in doctor.rs using Method Object pattern

[Tcode-Motion]

🎯 What: Refactored the excessively long execute function in cli/src/commands/doctor.rs.
💡 Why: The monolithic function was hard to read and maintain. Extracting state into a DoctorContext struct and breaking checks into individual methods significantly improves readability, testability, and adherence to clean code principles.
✅ Verification: Tested the refactored code using cargo check -p techscript_cli, cargo test -p techscript_cli, and verified full workspace safety with cargo test --workspace. All existing test cases pass smoothly. Code was automatically verified with code review tool.
✨ Result: execute is now clean and orchestrates checks via clear, domain-specific method calls on a DoctorContext object, dramatically improving code health and maintainability while preserving all behavior.

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PR created automatically by Jules for task 634770802771871498 started by @Tcode-Motion

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