docs: add VitePress site for RxJS Next

[benlesh]

Summary

Ports Jessica Sachs's VitePress documentation rewrite to the current master branch (RxJS Next / probable RxJS 9).

This uses #7588 as the primary source because it contains the more complete monorepo-integrated implementation. #7591 was useful as a later 7.x adaptation reference.

• adds the VitePress site as the rxjs.dev-next pnpm workspace app
• generates API documentation from the current public exports of all four Next packages
• adds an RxJS Next overview consistent with the current project charter and architecture
• type-checks API sources separately before TypeDoc generation
• keeps generated API Markdown and VitePress output out of Git
• removes the Nuxt UI coupling that prevented VitePress server rendering
• leaves runtime source and behavior unchanged

Jessica is credited as co-author on the port commit.

Verification

• pnpm run docs:build
• VitePress client build, server build, and page rendering pass
• TypeDoc reports 0 errors and 6 existing source-comment warnings

Follow-ups

Legacy stable-guide API links are narrowly exempted from VitePress's dead-link check until versioned deployment and redirect policy is decided. Work for 5.x, 6.x, and 8.x is intentionally deferred.