fix: include provider and model name in billing error message (#20510)

Merged via /review-pr -> /prepare-pr -> /merge-pr.

Prepared head SHA: 40dbdf62e8
Co-authored-by: echoVic <16428813+echoVic@users.noreply.github.com>
Co-authored-by: gumadeiras <5599352+gumadeiras@users.noreply.github.com>
Reviewed-by: @gumadeiras

src/agents/pi-embedded-subscribe.lifecycle-billing-error.e2e.test.ts

@@ -0,0 +1,35 @@
+import type { AssistantMessage } from "@mariozechner/pi-ai";
+import { describe, expect, it, vi } from "vitest";
+import { createStubSessionHarness } from "./pi-embedded-subscribe.e2e-harness.js";
+import { subscribeEmbeddedPiSession } from "./pi-embedded-subscribe.js";
+
+describe("subscribeEmbeddedPiSession lifecycle billing errors", () => {
+  it("includes provider and model context in lifecycle billing errors", () => {
+    const { session, emit } = createStubSessionHarness();
+    const onAgentEvent = vi.fn();
+
+    subscribeEmbeddedPiSession({
+      session,
+      runId: "run-billing-error",
+      onAgentEvent,
+      sessionKey: "test-session",
+    });
+
+    const assistantMessage = {
+      role: "assistant",
+      stopReason: "error",
+      errorMessage: "insufficient credits",
+      provider: "Anthropic",
+      model: "claude-3-5-sonnet",
+    } as AssistantMessage;
+
+    emit({ type: "message_update", message: assistantMessage });
+    emit({ type: "agent_end" });
+
+    const lifecycleError = onAgentEvent.mock.calls.find(
+      (call) => call[0]?.stream === "lifecycle" && call[0]?.data?.phase === "error",
+    );
+    expect(lifecycleError).toBeDefined();
+    expect(lifecycleError?.[0]?.data?.error).toContain("Anthropic (claude-3-5-sonnet)");
+  });
+});