fix(core): preserve provider metadata namespaces (#35817)

Co-authored-by: Aiden Cline <63023139+rekram1-node@users.noreply.github.com>
Co-authored-by: Aiden Cline <aidenpcline@gmail.com>

packages/core/test/session-runner-model.test.ts

@@ -53,6 +53,7 @@ describe("SessionRunnerModel", () => {
       expect(resolved).toMatchObject({ id: "api-test-model", provider: "test-provider" })
       expect(resolved.route).toMatchObject({
         id: "openai-responses",
+        providerMetadataKey: "openai",
         endpoint: { baseURL: "https://openai.example/v1" },
         defaults: {
           headers: { "x-test": "header" },
@@ -264,6 +265,7 @@ describe("SessionRunnerModel", () => {
 
       expect(resolved.route).toMatchObject({
         id: "anthropic-messages",
+        providerMetadataKey: "anthropic",
         endpoint: { baseURL: "https://anthropic.example/v1" },
       })
     }),