Move LLM Gateway docs to /llm-gateway/docs

[SebConejo]

Summary

• Publish the complete LLM Gateway documentation under /llm-gateway/docs/*.
• Make the new Gateway URLs canonical and keep internal navigation inside the namespace.
• Retain the original page files for the phase-one transition while the website still serves legacy /docs/* URLs.
• Add direct prefixed aliases without introducing a wildcard redirect.
• Identify the product as the Manifest LLM Gateway across navigation, metadata, and all documentation pages.
• Use natural Gateway terminology in prose while preserving public technical identifiers such as X-Manifest-*, mnfst_*, error messages, Docker images, and published integration names.
• Distinguish LLM Gateway Cloud, the self-hosted gateway, and Manifest Autofix without treating "Manifest" as a synonym for the Gateway.

Verification

• node scripts/check-coherence.mjs: GREEN (94 pages, 61 environment variables).
• npx mint dev: /llm-gateway/docs resolves to the Gateway introduction; representative Gateway deep links return 200.
• Copy audit: all 45 transition pages match their canonical /llm-gateway/docs/* copies.
• Namespace audit: Gateway canonicals and internal links stay under /llm-gateway/docs/*.
• docs.json parses successfully.
• git diff --check passes.

Known pre-existing issue

npx mint broken-links also parses references/backlog.md and stops on its existing MDX syntax error at line 32. That reference file is unchanged and is not part of the published navigation.