fix: prevent AI models from self-introducing in debate responses

[aiedwardyi]

Summary

• Add explicit system prompt instruction to skip self-introduction and jump straight into the topic
• Fixes Gemini producing empty/useless responses like "제미니입니다. 제공해주" (I'm Gemini. Please provide) instead of contributing to the discussion
• Applied to all models since any could waste tokens on self-introduction, especially in short response mode with Korean locale

Test plan

• Start a Korean short-mode debate and verify Gemini engages with the topic directly
• Confirm other models (Claude, GPT, Perplexity) also skip self-introduction
• Verify no regression in English debates