docs: add the Auto-fix API to the Gateway docs - #1150

Why

The Gateway is getting a standalone endpoint that repairs invalid OpenUI Lang without routing the request through generation (thesysdev/muse#599, thesysdev/coda#1024). Users who call a model directly need to find it from the Gateway docs and know what it takes, returns, and costs.

The endpoint ships with thesysdev/muse#599 and thesysdev/coda#1024. Merge this once those are deployed, so the page never describes something that does not answer.

What changes

• New page, Auto-fix API (gateway/api/auto-fix.mdx): endpoint, a complete example with the library spec import and the API key, the request fields, the three status values with a sample response for a fix and for a failed fix, the error codes with their meaning, limits, a pricing pointer, HTTP errors, and how calls appear in the console.
• Introduction: a third card under "Choose an API" and one bullet under "What OpenUI Gateway provides".
• Sidebar: Auto-fix API under APIs, after Conversations API.
• Reliability: a "New: Auto-fix API" callout at the top of the page, the table row updated to mention it, and one line under "What your application still controls" about fallback when a repair fails.
• Pricing: a short note under Gateway rates. Flat $0.02 per call that runs a fix, from Gateway Credits; a valid generation is free; no plan API call. The API page only links here.

Wording follows the existing pages: short sentences, the reader's side of the screen, and the same section order as the other API pages. The existing pages were edited in place without reformatting, since they are not prettier-formatted.

Check before merging

• The sample responses were captured from a local run and match the contract in the muse PR.
• Rendered locally on the docs dev server: intro cards, sidebar entry, the new page, the Reliability callout, and the Pricing note all display as intended.

🤖 Generated with Claude Code

Review round 1

Applied: no "program" anywhere (the API field is now generation on both sides); openUIlibraryVersion and customActions removed, library is the one input and takes openui.spec.json as the CLI writes it; full examples with imports; artifact limit line removed; "two attempts to fix the generation"; price stated only on the Pricing page.

Review round 2

Renamed the API from Sanitize to Auto-fix: page api/auto-fix.mdx, sidebar entry, card, callout, endpoint /v1/embed/auto-fix, console model name openui/auto-fix.

Conversation context

The Auto-fix API page also documents the optional messages field: the conversation that produced the generation, as { role, content } turns, used only to understand intent. Limits: 20 turns and 8,000 characters in total, oldest turns dropped first. Both code examples pass it, and the 400 row covers it. Pairs with muse #601 and coda #1026. (Folded in from #1162.)

Review round 3: the OpenAI chat shape, and the name loses its dash

The API is now the Autofix API, with no dash anywhere: the page is
gateway/api/autofix.mdx, the path is /v1/autofix, and the console model name
is openui/autofix. Every link and mention under docs/content follows.

The request and the answer are an OpenAI chat completion, so the page was
rewritten around that:

• There are two entry points. POST https://api.thesys.dev/v1/autofix for a
  plain HTTP call, and https://api.thesys.dev/v1/autofix/chat/completions,
  which is where an OpenAI SDK posts when /v1/autofix is its base URL. Same
  body, same answer.
• The primary example is the OpenAI Node SDK, with the cast the extra
  fix_summary field needs. A plain fetch example and a Python example
  follow.
• The conversation is no longer a separate messages field beside a
  generation: messages is the request, and the generation is the last
  assistant turn. The Request table says so, and the 400 row covers it.
• The answer section describes a chat completion: choices[0].message.content
  for the generation, fix_summary for status, fixed_errors and
  unfixed_errors.
• Streaming is not supported, listed in the Request table and in the 400
  row.

Checked on the local docs server: /docs/gateway/api/autofix renders, and no
page under docs/content links to auto-fix any more.