feat(backend): guard de fermeture "travail en cours" (#83)

Expose l'état du guard de sortie applicative (GetAppExitWorkGuardState) :
agents busy + tâches d'arrière-plan actives à travers tous les projets
ouverts, avec détails compacts pour la popup de confirmation. Le handler
CloseRequested d'app-tauri interroge ce guard avant de laisser la fenêtre
se fermer, et respecte la confirmation explicite de l'utilisateur
(EXIT_GUARD_CONFIRMED) pour ne pas la redemander en boucle.

QA vert (backend + frontend).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

crates/backend/src/dto.rs

@@ -9,12 +9,12 @@
 use serde::{Deserialize, Serialize};
 
 use application::{
-    AgentBackgroundTaskState, AgentTicketState, AppError, AttachLiveAgentOutput,
-    BackgroundTaskKindLabel, ConversationPreviewStatus, ConversationTurnWorkPreview,
-    ConversationWorkSummary, CreateProjectInput, CreateProjectOutput, GitGraphOutput, HealthInput,
-    HealthReport, LayoutKind, ListProjectsOutput, LiveSessionKind, LiveSessionSnapshot,
-    OpenProjectOutput, ProjectWorkState, StopLiveAgentOutput, TicketWorkSource, TicketWorkStatus,
-    TurnPage, TurnSource, TurnView,
+    AgentBackgroundTaskState, AgentTicketState, AppError, AppExitWorkGuardDetail,
+    AppExitWorkGuardState, AttachLiveAgentOutput, BackgroundTaskKindLabel,
+    ConversationPreviewStatus, ConversationTurnWorkPreview, ConversationWorkSummary,
+    CreateProjectInput, CreateProjectOutput, GitGraphOutput, HealthInput, HealthReport, LayoutKind,
+    ListProjectsOutput, LiveSessionKind, LiveSessionSnapshot, OpenProjectOutput, ProjectWorkState,
+    StopLiveAgentOutput, TicketWorkSource, TicketWorkStatus, TurnPage, TurnSource, TurnView,
 };
 use domain::{AgentBusyState, PageCursor, PageDirection, Project, ProjectId, TurnRole};
 
@@ -2275,6 +2275,111 @@ impl From<ProjectWorkState> for ProjectWorkStateDto {
     }
 }
 
+/// App-wide shutdown guard read model for the exit confirmation flow.
+#[derive(Debug, Clone, Serialize)]
+#[serde(rename_all = "camelCase")]
+pub struct AppExitWorkGuardStateDto {
+    /// Whether at least one active work item would be interrupted by app exit.
+    pub has_work_in_progress: bool,
+    /// Number of busy agents across all open projects.
+    pub busy_agent_count: usize,
+    /// Number of non-terminal background tasks across all open projects.
+    pub active_background_task_count: usize,
+    /// Total active work items.
+    pub total_work_count: usize,
+    /// Best-effort compact details for the confirmation dialog.
+    pub details: Vec<AppExitWorkGuardDetailDto>,
+}
+
+impl From<AppExitWorkGuardState> for AppExitWorkGuardStateDto {
+    fn from(state: AppExitWorkGuardState) -> Self {
+        Self {
+            has_work_in_progress: state.has_work_in_progress,
+            busy_agent_count: state.busy_agent_count,
+            active_background_task_count: state.active_background_task_count,
+            total_work_count: state.busy_agent_count + state.active_background_task_count,
+            details: state
+                .details
+                .into_iter()
+                .map(AppExitWorkGuardDetailDto::from)
+                .collect(),
+        }
+    }
+}
+
+/// One active work item contributing to [`AppExitWorkGuardStateDto`].
+#[derive(Debug, Clone, Serialize)]
+#[serde(rename_all = "camelCase", tag = "kind")]
+pub enum AppExitWorkGuardDetailDto {
+    /// A manifest agent is currently processing a turn.
+    BusyAgent {
+        /// Owning project id.
+        project_id: String,
+        /// Owning project display name.
+        project_name: String,
+        /// Agent id.
+        agent_id: String,
+        /// Agent display name.
+        agent_name: String,
+        /// Busy ticket id, when available.
+        ticket_id: Option<String>,
+    },
+    /// A first-class background task is queued, running or waiting.
+    ActiveBackgroundTask {
+        /// Owning project id.
+        project_id: String,
+        /// Owning project display name.
+        project_name: String,
+        /// Owning agent id.
+        agent_id: String,
+        /// Owning agent display name.
+        agent_name: String,
+        /// Stable task id.
+        task_id: String,
+        /// Lifecycle state.
+        state: String,
+        /// Kind discriminant.
+        task_kind: String,
+    },
+}
+
+impl From<AppExitWorkGuardDetail> for AppExitWorkGuardDetailDto {
+    fn from(detail: AppExitWorkGuardDetail) -> Self {
+        match detail {
+            AppExitWorkGuardDetail::BusyAgent {
+                project_id,
+                project_name,
+                agent_id,
+                agent_name,
+                ticket_id,
+            } => Self::BusyAgent {
+                project_id: project_id.to_string(),
+                project_name,
+                agent_id: agent_id.to_string(),
+                agent_name,
+                ticket_id: ticket_id.map(|id| id.to_string()),
+            },
+            AppExitWorkGuardDetail::ActiveBackgroundTask {
+                project_id,
+                project_name,
+                agent_id,
+                agent_name,
+                task_id,
+                state,
+                kind,
+            } => Self::ActiveBackgroundTask {
+                project_id: project_id.to_string(),
+                project_name,
+                agent_id: agent_id.to_string(),
+                agent_name,
+                task_id: task_id.to_string(),
+                state: background_state_label(state).to_owned(),
+                task_kind: background_kind_label_from_work_state(kind).to_owned(),
+            },
+        }
+    }
+}
+
 /// Request DTO for `attach_live_agent`: bind an already-running agent session to
 /// a visible layout cell without spawning a new process.
 #[derive(Debug, Clone, Deserialize)]