fix(image): add response-header timeout and idempotent retry

Give the image client a configurable ResponseHeaderTimeout (default 4m,
capped at the overall timeout) so a stalled upstream fails fast, and
retry such timeouts when an idempotency key is set so a slow-but-safe
request can recover instead of terminating. Raise the Next.js API proxy
maxDuration to 1200s to accommodate long generations.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

server/internal/infrastructure/piagent/image_generation_test.go

@@ -347,3 +347,41 @@ func TestImageClientDoesNotRetryRequestTimeout(t *testing.T) {
 		t.Fatalf("expected timeout to fail fast without retry, got %d calls", calls)
 	}
 }
+
+func TestImageClientRetriesIdempotentResponseHeaderTimeout(t *testing.T) {
+	calls := 0
+	var keys []string
+	server := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		calls++
+		keys = append(keys, r.Header.Get("Idempotency-Key"))
+		if calls == 1 {
+			time.Sleep(80 * time.Millisecond)
+			return
+		}
+		w.Header().Set("Content-Type", "application/json")
+		_, _ = w.Write([]byte(`{"data":[{"url":"https://example.com/recovered.png"}]}`))
+	}))
+	defer server.Close()
+
+	client := NewImageClient(ImageClientOptions{BaseURL: server.URL, APIKey: "test-key"})
+	transport, ok := client.client.Transport.(*http.Transport)
+	if !ok {
+		t.Fatalf("expected http transport, got %T", client.client.Transport)
+	}
+	transport.ResponseHeaderTimeout = 20 * time.Millisecond
+	client.client.Timeout = time.Second
+
+	image, err := client.Generate(context.Background(), "create an image", ImageRequestOptions{Model: "gpt-image-2", IdempotencyKey: "same-generation"})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if image.URL != "https://example.com/recovered.png" {
+		t.Fatalf("expected recovered image, got %#v", image)
+	}
+	if calls != 2 {
+		t.Fatalf("expected one retry after timeout, got %d calls", calls)
+	}
+	if len(keys) != 2 || keys[0] != "same-generation" || keys[1] != "same-generation" {
+		t.Fatalf("expected retry to keep idempotency key, got %#v", keys)
+	}
+}