Migrate docs demos to OpenUI Cloud

[zahlekhan]

Summary

• migrate every hosted LLM-backed docs demo to OpenUI Cloud, including the OSS and Markdown modes
• split Chat OSS, Chat Cloud, Compare Markdown, Compare OSS, Compare Cloud, Playground, and GitHub across seven dedicated server-side API keys
• keep managed Cloud modes on Responses and frontend tokens while routing OSS, Markdown, Playground, and GitHub through OpenUI Cloud Chat Completions
• send both managed Cloud generation workloads through one /api/openui-cloud/chat route with an allowlisted workload selector
• preserve existing streaming, tools, abort behavior, credit-exhaustion handling, prompts, and Playground request behavior
• document the seven workload keys in the README and environment example, with strict same-origin validation for managed Cloud routes

Why

OpenUI Cloud is the generic LLM provider for the hosted demos. Dedicated keys per workload make usage and spend independently attributable, including the separate OSS and Cloud modes within Chat and all three Compare workloads.

Validation

• pnpm --filter @openuidev/docs types:check
• pnpm --filter @openuidev/docs build
• targeted Prettier and ESLint checks for changed files
• production runtime checks for fail-closed key handling, workload-key selection, and upstream HTTP status propagation
• git diff --check

The full docs-wide format and lint commands retain existing failures in untouched files; changed files pass their focused checks. Provider-side usage attribution still requires a smoke test with the seven deployment keys.