I still suspect a power issue here. The difference between Battery alone Vs powered via USB as well aims us clearly at a power issue.
I would see if [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] was able to see the battery when you connect the iPod to your Mac. I’ve never tried so I’m not sure. Post a question to Chris maybe he can tell you if it would work (his email is in the link). Post a snapshot here for us to see if it works! Maybe it will offer us a clue on what is happening.