docs: improve README with badges, nav links, better quick start, and contributing section

[justrach]

Brings the README up to par with popular OSS repos.

Changes:

• Add 5 shields.io badges (version, license, stars, Zig, MCP)
• Centered hero with tagline and nav links
• Binary download as primary install option (lower friction than build-from-source)
• Collapse per-client config into <details> dropdowns
• Add Contributing section (was missing entirely)
• Move Requirements inline with Quick Start
• Link LICENSE file from License section