feat(chat): wire follow-up chat UI + add LLM setup docs

[Void-Anvesha]

Description

Add a minimal follow-up chat handler to the frontend and document safe LLM/API-key setup for contributors.

• Wire the chat Send button and Enter key in frontend/index.html so the chat pane sends POSTs to /chat/.
• Send richer chat payload (code, latest analysis/context, simple history) to help backend produce better replies.
• Add guidance to CONTRIBUTING.md describing how to create a local backend/.env, where to set LLM_API_KEY, and CI/deploy best-practices for secrets.
• Small housekeeping: expose a simple window.chatHistory to collect recent messages used as context.

Notes:

• Default behavior remains rule-based when LLM_ENABLED=false.
• Ensure no secrets are committed: .env is ignored by .gitignore. If you accidentally committed backend/.env, remove it from the commit and rotate the key before opening this PR.

Related Issue

Fixes #

Type of change

• Bug fix
• New feature / enhancement
• Documentation update
• Test addition
• Refactor

Checklist

• I have read CONTRIBUTING.md
• My branch is up to date with main
• I have run pytest -v and all tests pass
• I have not introduced duplicate issues or features
• My PR title follows the format: feat/fix/docs/test: short description
• I have added tests for new features (Level 2 and 3 issues)
• No hardcoded secrets or API keys in my code (If backend/.env exists locally, ensure it's NOT staged for commit)
• This PR is linked to a GSSoC 2026 issue

Screenshots:

Before: n/a
After: chat input wired; Send/Enter submits; assistant replies appear in chat pane.

Test evidence

# Run backend locally and verify:
cd backend
python -m uvicorn app.main:app --reload

# Then in browser open frontend/index.html (or use curl)
curl -s -X POST http://localhost:8000/chat/ -H "Content-Type: application/json" \
  -d '{"message":"Is there an issue with this code?","code":"print(hello);;","context":"","history":[]}'

# Expected: backend responds (rule-based fallback or LLM reply if LLM enabled)

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[imDarshanGK]

@Void-Anvesha
issue number and add demo video showing the working features

[Void-Anvesha]

#1659