refactor(desktop-task): extract recovery select query and scan task status

Pull the recovered-task SELECT into a dedicated helper so the column list and
lease-expiry filter are testable, add a status column to the scan so logs
report the real task state, and log scan/iterate failures with the client and
recovery mode for observability.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

server/internal/tenant/app/desktop_task_service_test.go

@@ -0,0 +1,63 @@
+package app
+
+import (
+	"regexp"
+	"strings"
+	"testing"
+)
+
+func TestDesktopTaskRecoverySelectQueryMatchesRecoveredLeaseScanOrder(t *testing.T) {
+	t.Parallel()
+
+	query := desktopTaskRecoverySelectQuery(desktopTaskRecoveryModeStartup)
+	gotColumns := recoverDesktopTaskSelectColumns(query)
+	wantColumns := []string{
+		"desktop_id",
+		"workspace_id",
+		"kind",
+		"status",
+		"active_attempt_id",
+	}
+
+	if len(gotColumns) != len(wantColumns) {
+		t.Fatalf("recover select columns = %v, want %v", gotColumns, wantColumns)
+	}
+	for index := range wantColumns {
+		if gotColumns[index] != wantColumns[index] {
+			t.Fatalf("recover select columns = %v, want %v", gotColumns, wantColumns)
+		}
+	}
+}
+
+func TestDesktopTaskRecoverySelectQueryLeaseExpiryFiltersExpiredLeases(t *testing.T) {
+	t.Parallel()
+
+	query := desktopTaskRecoverySelectQuery(desktopTaskRecoveryModeLeaseExpiry)
+
+	for _, fragment := range []string{
+		"AND lease_expires_at IS NOT NULL",
+		"AND lease_expires_at < NOW()",
+		"FOR UPDATE",
+	} {
+		if !strings.Contains(query, fragment) {
+			t.Fatalf("recover lease-expiry query missing %q: %s", fragment, query)
+		}
+	}
+}
+
+func recoverDesktopTaskSelectColumns(query string) []string {
+	re := regexp.MustCompile(`(?is)select\s+(.*?)\s+from\s+desktop_tasks`)
+	match := re.FindStringSubmatch(query)
+	if len(match) != 2 {
+		return nil
+	}
+
+	rawColumns := strings.Split(match[1], ",")
+	columns := make([]string, 0, len(rawColumns))
+	for _, rawColumn := range rawColumns {
+		column := strings.TrimSpace(rawColumn)
+		column = strings.Fields(column)[0]
+		columns = append(columns, column)
+	}
+	return columns
+}