fix: replace pgrep with tmutil status for more accurate Time Machine backup detection and add new tests for this logic.

lib/clean/system.sh

@@ -213,8 +213,8 @@ clean_time_machine_failed_backups() {
         return 0
     fi
 
-    # Skip if backup is running
-    if pgrep -x "backupd" > /dev/null 2>&1; then
+    # Skip if backup is running (check actual Running status, not just daemon existence)
+    if tmutil status 2>/dev/null | grep -q "Running = 1"; then
         if [[ "$spinner_active" == "true" ]]; then
             stop_section_spinner
         fi