fix(server): complete generator task when thread settles or project ready

Treat a generator task as completed when it produces artifacts, when a
task message reaches a terminal state, or when the project is ready —
even if the project is still exploring another concurrent thread. Adds
generatorTaskMessageCompleted to classify terminal task messages and
covers ready-without-messages and concurrent-thread cases with tests.

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

server/internal/application/generator_task.go

@@ -384,7 +384,7 @@ func generatorTaskMetadataFromMessages(messages []design.Message, taskID string)
 func generatorTaskStatus(project design.Project, taskID string) string {
 	messages := project.Messages
 	status := "submitted"
-	completed := false
+	completed := len(generatorTaskArtifacts(messages, taskID)) > 0
 	for _, message := range messages {
 		if message.ThreadID != taskID {
 			continue
@@ -392,9 +392,11 @@ func generatorTaskStatus(project design.Project, taskID string) string {
 		if message.Role == "error" || message.Status == "failed" {
 			return "failed"
 		}
+		if generatorTaskMessageCompleted(message) {
+			completed = true
+		}
 		switch message.Status {
 		case "success", "cancelled":
-			completed = true
 		case "running", "streaming", "submitted":
 			status = "submitted"
 		}
@@ -405,15 +407,30 @@ func generatorTaskStatus(project design.Project, taskID string) string {
 	if project.Status == design.StatusFailed {
 		return "failed"
 	}
-	if project.Status == design.StatusExploring {
-		return status
-	}
-	if len(generatorTaskArtifacts(messages, taskID)) > 0 || completed {
+	if completed || project.Status == design.StatusReady {
 		return "completed"
 	}
 	return status
 }
 
+func generatorTaskMessageCompleted(message design.Message) bool {
+	status := strings.ToLower(strings.TrimSpace(message.Status))
+	if status != "success" && status != "cancelled" {
+		return false
+	}
+	name := strings.TrimSpace(message.Name)
+	if name == "agent_planner" || name == "generator_task" {
+		return false
+	}
+	if isToolArtifactsMessage(message) {
+		return true
+	}
+	return name == "canvas_action" ||
+		name == "text_extraction" ||
+		name == "mockup_model" ||
+		strings.TrimSpace(message.Role) == "assistant"
+}
+
 func generatorTaskHasActiveCanvasWork(project design.Project, taskID string) bool {
 	taskID = strings.TrimSpace(taskID)
 	lastThreadID := strings.TrimSpace(project.LastThreadID)