Refactor LLM route-first provider API (#28523)

packages/llm/test/provider/openai-responses-cache.recorded.test.ts

@@ -2,14 +2,13 @@ import { describe, expect } from "bun:test"
 import { Effect } from "effect"
 import { LLM } from "../../src"
 import { LLMClient } from "../../src/route"
-import * as OpenAIResponses from "../../src/protocols/openai-responses"
+import * as OpenAI from "../../src/providers/openai"
 import { LARGE_CACHEABLE_SYSTEM } from "../recorded-scenarios"
 import { recordedTests } from "../recorded-test"
 
-const model = OpenAIResponses.model({
-  id: "gpt-4.1-mini",
+const model = OpenAI.configure({
   apiKey: process.env.OPENAI_API_KEY ?? "fixture",
-})
+}).responses("gpt-4.1-mini")
 
 // OpenAI caches prefixes automatically once they cross the 1024-token threshold;
 // `CacheHint` is a no-op for the wire body. The stable signal is the