fix(provider): serialize Mistral prompt cache keys (#38448)

packages/core/test/provider-mistral.test.ts

@@ -0,0 +1,28 @@
+import { createMistral } from "@ai-sdk/mistral"
+import { expect, test } from "bun:test"
+
+test("Mistral sends promptCacheKey as prompt_cache_key", async () => {
+  let body: Record<string, unknown> | undefined
+  const mockFetch = Object.assign(
+    async (_input: Parameters<typeof fetch>[0], init?: RequestInit) => {
+      body = JSON.parse(String(init?.body))
+      return Response.json({
+        id: "response-1",
+        created: 0,
+        model: "mistral-large-latest",
+        object: "chat.completion",
+        choices: [{ index: 0, message: { role: "assistant", content: "Hello" }, finish_reason: "stop" }],
+        usage: { prompt_tokens: 1, completion_tokens: 1, total_tokens: 2 },
+      })
+    },
+    { preconnect: fetch.preconnect },
+  )
+  const model = createMistral({ apiKey: "test", fetch: mockFetch })("mistral-large-latest")
+
+  await model.doGenerate({
+    prompt: [{ role: "user", content: [{ type: "text", text: "Hello" }] }],
+    providerOptions: { mistral: { promptCacheKey: "session-123" } },
+  })
+
+  expect(body?.prompt_cache_key).toBe("session-123")
+})