feat(piagent): batch-generate images in one call when generators share a prompt

When multiple image-generator tasks carry the same brief, request all
images from a single GPT Image call with Count=N instead of firing one
call per image. Adds directImageBatchCount/Prompt detection, batch
(incremental) generation paths, and folds the planned count into the
idempotency key. Disables the streaming plan probe for multi-image
requests.

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

server/internal/infrastructure/piagent/design_agent_test.go

@@ -270,6 +270,64 @@ func TestDesignAgentImageGeneratorModeCallsImageModelDirectly(t *testing.T) {
 	}
 }
 
+func TestDesignAgentImageGeneratorModeBatchesSamePromptCount(t *testing.T) {
+	runner := &recordingRunner{}
+	creative := &recordingCreativeAgent{}
+	imageGenerator := &fakeImageGenerator{}
+	agent := NewDesignAgent(runner, imageGenerator, creative)
+	var emitted []design.Node
+
+	plan, err := agent.PlanIncremental(context.Background(), design.AgentRequest{
+		Project: design.Project{
+			ID: "project-image-generator",
+			Nodes: []design.Node{
+				{
+					ID:        "generator-1",
+					Type:      design.NodeTypeImage,
+					Tone:      "image-generator",
+					Status:    "generating",
+					LayerRole: "image-generator",
+					Width:     512,
+					Height:    512,
+				},
+			},
+		},
+		Prompt:     "画一只蓝色小鸟",
+		Mode:       "image-generator",
+		ImageModel: "gpt-image-2",
+		ImageSize:  "1024x1024",
+		TaskPlan: design.AgentTaskPlan{
+			Intent:     "image",
+			ImageCount: 2,
+			ImageTasks: []design.AgentImageTask{
+				{Title: "蓝色小鸟 方案 1", Brief: "画一只蓝色小鸟"},
+				{Title: "蓝色小鸟 方案 2", Brief: "画一只蓝色小鸟"},
+			},
+		},
+	}, func(result design.AgentImageGenerationResult) error {
+		emitted = append(emitted, result.Node)
+		return nil
+	})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if runner.calls != 0 || creative.buildCalls != 0 {
+		t.Fatalf("expected direct image generator mode, runner=%d build=%d", runner.calls, creative.buildCalls)
+	}
+	if imageGenerator.callCount() != 1 {
+		t.Fatalf("expected one batched image request, got %d", imageGenerator.callCount())
+	}
+	if imageGenerator.opts.Count != 2 {
+		t.Fatalf("expected image request n/count 2, got %#v", imageGenerator.opts)
+	}
+	if len(emitted) != 2 || len(plan.GeneratedNodes) != 2 {
+		t.Fatalf("expected two generated nodes, emitted=%#v plan=%#v", emitted, plan.GeneratedNodes)
+	}
+	if plan.GeneratedNodes[0].ID != "generator-1" || plan.GeneratedNodes[1].ID == "generator-1" {
+		t.Fatalf("expected first node to replace generator and second to be separate, got %#v", plan.GeneratedNodes)
+	}
+}
+
 func (g *fakeImageGenerator) callCount() int {
 	g.mu.Lock()
 	defer g.mu.Unlock()
@@ -635,6 +693,7 @@ func TestGeneratedImageNodeFromImageGeneratorSlotBecomesRegularImage(t *testing.
 			Tone:      "image-generator",
 			Status:    "generating",
 			LayerRole: "image-generator",
+			ParentID:  "generator-parent",
 			Width:     320,
 			Height:    240,
 		},
@@ -647,6 +706,9 @@ func TestGeneratedImageNodeFromImageGeneratorSlotBecomesRegularImage(t *testing.
 	if node.LayerRole != "" || node.Tone != "visual" || node.Status != "success" {
 		t.Fatalf("expected regular completed image node, got %#v", node)
 	}
+	if node.ParentID != "" {
+		t.Fatalf("expected completed image generator node to clear parent id, got %#v", node)
+	}
 }
 
 func TestDesignAgentDoesNotRunFallbackAfterImageTimeout(t *testing.T) {