[FEATURE]: Add GitHub Star Badge to Navbar for Social Proof

### Feature and its Use Cases

I propose adding a GitHub repository link with a dynamic star counter to the top navigation bar (ideally next to the theme toggle).

Why this matters:
Social Proof: It instantly communicates trust and credibility to developers and tech-savvy users evaluating the tool.
Conversion: A persistent, visible CTA in the navbar reduces the friction for users to drop a star, helping the project grow its visibility on GitHub.

### Additional Context

_No response_

### Code of Conduct

- [x] I have joined the [Discord server](https://discord.gg/hjUhu33uAn) and will post updates there
- [x] I have searched existing issues to avoid duplicates