docs: document OpenUI Cloud Responses and Chat Completions APIs

[vishxrad]

What changed

• Add dedicated Responses API and Chat Completions API guides.
• Align both guides around the same client setup, managed request, streaming/rendering, history, tools, artifacts, BYOK, and API-choice structure.
• Add one shared Component Library feature guide with parallel Responses and Chat Completions examples for the built-in library and custom libraries.
• Keep protocol-specific behavior explicit: Chat passthrough and self-hosted prompt assembly; Responses persistent conversations and hosted tools.
• Add the API and Component Library guides to the OpenUI Cloud navigation.
• Update the Cloud architecture and quickstart docs to distinguish the Responses and Chat Completions lifecycles.

Why

The Responses API guidance was distributed across the Cloud docs, while the newly supported Chat Completions surface had no first-class OpenUI documentation. The parallel structure makes both protocols discoverable and lets readers compare equivalent workflows. Shared component-library guidance now has one canonical location instead of drifting between API pages.

Developer impact

Developers can start from a protocol-specific guide, migrate an existing OpenAI Chat Completions integration, or choose Responses for Cloud-managed capabilities. Both API guides point to the same built-in and custom component-library workflow, with API-specific backend request examples.

Validation

• pnpm --filter @openuidev/docs types:check
• pnpm --filter @openuidev/docs build
• Prettier on changed docs
• git diff --check
• GitHub Build JS, build-examples, and Vercel checks

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Project	Deployment	Actions	Updated (UTC)
openui-docs	Ready	Preview	Aug 13, 2026 1:13pm