The iTunes app on Macs was discontinued and replaced when macOS Catalina was released. It cannot be installed on a Mac running Catalina, Big Sur or Monterey (including your 12.6). See: What happened to iTunes? - Apple Support
Also, syncing a device with iCloud does not require use of any computer.
An iPod touch 5th generation cannot be updated beyond iOS 9.3.5 but many iCloud syncing options work with that. iCloud Photos syncing for example, works with iOS 8.3 and later. See: System requirements for iCloud - Apple Support
You may want to reply with more information about what it is that you want to sync with iCloud.