can't get my iTunes songs/playlists on my new iPod classic

got a new (refurbished) iPod Classic, software fully updated, and have connected it to my iTunes (Windows 11, software fully updated as well). can't get my iTunes songs or playlists to download to the iPod - seems like i've tried everything. if it matters, the music (and library) are on an external drive, though iTunes is successfully working with that. helpful ideas or instructions?

on a separate issue, on a Windows 11 machine i can't get iTunes to see my whole library on the same external drive. it only sees some, but not all, of my music. any thoughts here would be appreciated.