An API reference in the forge: /api renders the forge's OpenAPI spec (and an app's own, if it serves one) — endpoints by area, schemas, and try it as yourself #7583

Part of #7578.

What exists: the spec is generated (src/contract/openapi.ts) and served at /api/v1/openapi.json, but nothing renders it.

Build:

• /api: endpoints grouped by area, with search, the method and path, and parameters and bodies as readable schemas. Try it sends the request with your own session or a token you pick, and shows the response and its Server-Timing.
• An app's API page: if an app serves /openapi.json, its page gets an API tab that renders it the same way.
• Rendering is server-side and works with no JavaScript. Try it is progressive. No CDN: anything vendored loads only on /api.
• The same in the terminal app: an API screen that lists endpoints and runs a GET.

Tests: every route in the contract appears on /api; Try it on a GET returns 200 for a signed-in person; an app with /openapi.json gets the tab.

Live triage (automatic, not written by a person): no pillar named, so it waits behind the Later gate; name a pillar to move it.