Restructure docs around use cases (#66)

Restructure docs around use cases (#66)

* Restructure docs around use cases

Replace the single Integrations page with four dedicated use case pages
(Browser Extension, Coding Tools, Apps & SDKs, Self-Hosted) so each
audience has a clear path through the docs.

- Rewrite introduction around four user contexts with cards
- Simplify quickstart to be tool-neutral
- Add Use Cases navigation group in mint.json
- Update README links to point to new docs pages
- Replace demo.gif with comparison.png
- Remove duplicate h1 headings (Mintlify renders frontmatter title)
- Remove Copilot from platform lists per positioning doc

* Sync docs and README with website messaging

- Update tagline to "AI gets the context. Not your secrets."
- Add trust statement and detection stats (30+ types, 24 languages)
- Rename use cases to match website: Chat, Apps, Coding Tools, API Integration
- Reorder use cases consistently across docs and README
- Replace comparison image with refined rose/teal design
- Add light/dark mode image support for GitHub and Mintlify

* Improve dark mode text contrast in comparison image