Playlists show on desktop but not on laptop signed in to same account

I have iTunes on my desktop with music sorted into about 15 different playlists. I also have all of it on an iPod which I use as a backup.

I recently got a laptop, downloaded iTunes on to it, signed in with my AppleID and found that while all the music is on there, none of my playlists are showing. Both the desktop and laptop are Windows.

I have checked, and haven't hidden the playlists accidentally. My question is, is there any way to have the playlists restored? Would doing a reverse sync from the iPod work, or would that just confuse the issue even further?