Bug: Interactive invoke of @claude not working

Description

Interactive invocation of @claude in GitHub issue comments is not functioning properly. When users mention @Claude in issue comments expecting an AI response, the system does not respond.

Reproduction Steps

1. Go to a GitHub issue in the dotCMS/infrastructure-as-code repository
2. Post a comment mentioning @Claude with a request
3. Observe that no AI response is generated

Actual Behavior

• User posted: "@Claude take a stab at a plan for this. Remember we just need to get lookups below 10. We don't have to get every include: flattened"
• No AI response was generated
• The interactive invoke functionality appears to be broken

Expected Behavior

@claude should respond to interactive invocations in GitHub issue comments with relevant assistance and planning

Evidence

• Original issue: https://github.com/dotCMS/infrastructure-as-code/issues/6448
• Specific comment: https://github.com/dotCMS/infrastructure-as-code/issues/6448#issuecomment-3145383735
• Comment timestamp: 2025-08-01T18:14:13Z
• User: @sfreudenthaler (MEMBER)

Impact

• Users cannot get AI assistance directly in GitHub issues
• Workflow interruption when expecting interactive AI help
• May affect productivity for infrastructure planning tasks

Environment

• Repository: dotCMS/infrastructure-as-code
• Issue type: SPF record optimization planning
• User role: Repository member

Next Steps

• Investigate why @claude mentions are not triggering AI responses
• Check ai-workflows configuration for GitHub integration
• Test @claude invocation in different repositories/contexts
• Verify webhook and authentication setup
• Implement fix and verify functionality works across repositories

Start with the ai-workflows configuration and GitHub integration used for interactive @claude mentions. Reproduce the comment from dotCMS/infrastructure-as-code issue #6448, then inspect webhook and authentication behavior across repositories and contexts. Done means @claude comments trigger a relevant response reliably and the behavior is verified in the affected workflow.