feat(api): reshape /api/sync/status for phase-aware progress

Replaces detail_fill_progress ({Done, Total}) with progress ({Phase,
Done, Total}), and adds workouts_pending (mirroring
activities_pending_details) from the new CountActivitiesMissingWorkout.
Frontend types updated to match -- GarminConnection.tsx is intentionally
left broken by this commit alone; it's fixed in the next commit that
adds SyncModal.

backend/internal/api/api_test.go

@@ -664,6 +664,48 @@ func TestSyncReset_DeletesActivitiesAndBackfillEndpointIsGone(t *testing.T) {
 	}
 }
 
+func TestSyncStatus_ReportsPhaseAwareProgressAndWorkoutsPending(t *testing.T) {
+	s, db, userID := newTestServer(t)
+	ctx := newCtx()
+
+	workoutID := int64(555)
+	if _, err := db.UpsertActivity(ctx, userID, store.Activity{
+		GarminActivityID: 1, WorkoutID: &workoutID,
+		StartTimeUTC: "2026-07-11 06:00:00", RawJSON: "{}",
+	}); err != nil {
+		t.Fatalf("UpsertActivity: %v", err)
+	}
+
+	rec := doJSON(t, s.Router(), http.MethodGet, "/api/sync/status", nil)
+	if rec.Code != http.StatusOK {
+		t.Fatalf("status = %d, body = %s", rec.Code, rec.Body.String())
+	}
+	var resp struct {
+		InProgress bool `json:"in_progress"`
+		Progress   struct {
+			Phase string `json:"Phase"`
+			Done  int    `json:"Done"`
+			Total int    `json:"Total"`
+		} `json:"progress"`
+		ActivitiesPendingDetails int `json:"activities_pending_details"`
+		WorkoutsPending          int `json:"workouts_pending"`
+	}
+	unmarshalBody(t, rec, &resp)
+
+	if resp.InProgress {
+		t.Error("in_progress = true, want false (nothing running)")
+	}
+	if resp.Progress.Phase != "idle" {
+		t.Errorf("progress.Phase = %q, want %q", resp.Progress.Phase, "idle")
+	}
+	if resp.ActivitiesPendingDetails != 1 {
+		t.Errorf("activities_pending_details = %d, want 1", resp.ActivitiesPendingDetails)
+	}
+	if resp.WorkoutsPending != 1 {
+		t.Errorf("workouts_pending = %d, want 1", resp.WorkoutsPending)
+	}
+}
+
 func TestProgression_ReturnsSortedTimeSeries(t *testing.T) {
 	s, db, userID := newTestServer(t)
 	ctx := newCtx()