Backend Field Naming: Rename example_name to code_example_name for clarity

[Wirasm]

Problem

The current backend uses as the field name for AI-generated code example titles, which causes confusion:

1. Generic naming: is vague and doesn't clearly indicate it's for code examples
2. Frontend confusion: The frontend has to map between , ]2;]1;, and fallback logic
3. API clarity: API consumers need to understand that contains the AI-generated descriptive title

Current Implementation

Backend generates:

• example_name: "Create and Use a Tool" (AI-generated descriptive title)
• title: "Create and Use a Tool" (copies from example_name)

Logs show:

Generated code example summary - Name: 'Create and Use a Tool', Summary length: 251
Generated code example summary - Name: 'Create Custom Tool with Preparation', Summary length: 343

Proposed Solution

Rename example_name → code_example_name for clarity:

Files to update:

• code_extraction_service.py (lines 1479, 1483, 1498)
• code_storage_service.py (line 601)
• Database schema/migration
• TypeScript interfaces
• API documentation

Benefits

• ✅ Clear field naming that indicates purpose
• ✅ Better API documentation
• ✅ Reduced frontend confusion
• ✅ More maintainable code

Impact

• Database: Requires migration if data exists
• Frontend: Simple TypeScript interface update
• API: Update response mapping

Low risk change that significantly improves code clarity.

[Wirasm]

even better might be code_example_title

[thsconsult]

@claude analyze this issue and provide implementation guidance