Implement scroll-to-bottom button in chat when scrolled up

[Kishalll]

🔗 Related Issue

Closes #423

📝 What does this PR do?

Implements a floating scroll-to-bottom button in the chat interface.

• The button smoothly fades in using a ChevronDown icon when a user scrolls up past a 100px threshold.
• Clicking the button smoothly scrolls the user back to the newest messages.
• Refines the auto-scroll behavior so it only pulls the user down on new messages if they are already
near the bottom (within 150px), preventing disruptive jumps if they are reading past chat history.

🗂️ Type of Change

• 🐛 Bug fix
• ✨ New feature
• 🔧 Refactor / code cleanup
• 📝 Documentation update
• 🎨 UI / styling change
• ⚙️ CI / tooling / config change
• 🧪 Tests

🧪 How was this tested?

• Ran the backend locally ( uvicorn app.main:app --reload )
• Ran the frontend locally ( npm run dev inside frontend/ )
• Tested the affected API endpoints manually
• Added / updated tests

⚠️ Anything to flag for reviewers?

N/A

✅ Self-Review Checklist

• My branch is based on dev , not main
• I have not added any secrets / API keys
• I have not modified main branch or any HuggingFace deployment config
• My code follows the existing style (no unnecessary formatting changes)
• I have updated relevant docs / comments if needed

[Kishalll]

@param20h pls review

[Kishalll]

@param20h resolved conflicts pls review