docs: transform the web app into a Type Testing Cookbook

[martyy-code]

Description

Transform apps/web from a simple demo into a comprehensive Type Testing Cookbook. Each page = one use case: the code being tested, the type assertion, and the exact TypeScript error produced when the test fails.

Why

expect-type has 63M weekly downloads but no docs site. The web app is a unique asset: interactive, searchable, with real error output. It should be the first place a developer lands when learning type testing.

Acceptance criteria

• Landing page: use case categories (special types, unions, generics, etc.)
• Each use case: live code, the assertion, the error message
• Search by type pattern or use case
• Exportable as copy-paste snippets

Risks

• Medium. Requires sustained content effort beyond code. Consider contribution workflow.

Related

• apps/web