feat: improve sidebar UI with distinct sections and better empty states

[github-roushan]

Describe Your Changes

• Add distinct backgrounds for Projects and Chats sections
• Add proper spacing and padding between sections
• Fix empty state logic to show "No threads yet" when all threads are in projects

Fixes Issues

• Closes #

Self Checklist

• [ ] Added relevant comments, esp in complex areas
• [ ] Updated docs (for bug fixes / features)
• [ ] Created issues for follow-up changes or refactoring needed