Hello S1P1G1,
Thank you for using Apple Support Communities. Based on your post, you can't sync your music on your iPod Classic.
To make sure we're on the same page, you are a member of Apple Music, but have downloaded/purchased content within your iTunes Library and you are unable to sync content to your iPod Classic. Is that right?
It could be related to the fact that the iPod Classic isn't a supported device with Apple Music: Join Apple Music on your iPhone, iPad, iPod touch, Mac, or PC
What happens exactly when you attempt to sync the iPod Classic with your library using these steps: Sync your iPhone, iPad, or iPod using your computer
Any errors? Does the computer recognize the iPod Classic?
Hoping to hear back, take care.