docs(skills): add /api-client — typed client recipe for response routes - #540

What

Adds a new skill, /api-client, that teaches consumers how to consume their own path.json() response-route APIs from first-party TypeScript with a typed client — and ships a ~50-line copy-paste helper that does it.

Follow-up to #539 (bare-T + RFC 9457 problem+json). It's a recipe, not a new framework export: the helper composes existing public exports (RouteResponse, ExtractParams, createReverse). Docs-only — no runtime or public-API change.

Why

Today, consuming your own API with types means hand-rolling a client per app (the test-app's api-shop-client.ts is ~105 lines of it), and the default consumer who skips that gets fetch(url).then(r => r.json()) → any. The recipe collapses that to:

const api = createApiClient(apiShopPatterns, routes, { baseUrl });
await api.health.get();                            // no params → callable bare
await api.product.get({ params: { productId } });  // params typed + required
//    ^ result is the bare payload (RouteResponse), not `any`, no `.data`

• Output typed from the handler's return (RouteResponse), no codegen.
• Path params required + typed from the route pattern; missing/misspelled param = compile error.
• Errors throw a typed ApiError carrying the ProblemDetails body.

Scope call-out (deliberate)

The typed client is a first-party TypeScript convenience — it needs your route types. External/third-party consumers use the plain wire directly (bare JSON + application/problem+json), which needs no client. Language-agnostic OpenAPI generation is intentionally deferred as the separate third-party lever. The skill states this explicitly so nobody mistakes the recipe for a third-party SDK.

Verification

The helper was compile-verified against the e2e/test-app api-shop routes (temporary type-test, since removed): required-param enforcement, no-arg paramless routes, typed .post({ body }), and @ts-expect-error on unknown routes / wrong param names. typecheck, lint, format all green.

Surface

• skills/api-client/SKILL.md (new)
• skills/rango/SKILL.md — indexed in the skill table
• skills/response-routes/SKILL.md — cross-linked ("Consuming response routes")