Apple Music not seeing my iPod 6 or 7 Classic & I'm using Windows 11

Ok, how do I do that? Remember I'm new to Apple Music and Apple Devices as of today so go gentle on me :-)

I see the song fine in Apple Music and I see the songs on my iPod ... so I do I get the song over to my iPod. Thanks.

Was able to follow those instructions. It appears that I'm seeing music on my iPod where as I want to see music inside of Apple Music to move over to my iPod. So I still need help. I went thru the music and don't see the new song I downloaded on this screen. I've gone thru the artist and also did a search. It's like I'm missing a step ... as in how can I get it to display music inside of Apple Music.

BTW thanks for all the help so far

I've made a lot of progress and also very close to getting music from Apple Music on a Windows 11 PC to my iPod but it's like I need one more step. I think I replied to one of my msgs and not the whole group. Hope this doesn't seem like a double post.

So, I was able to download a song into Apple Music, I can see it, I can play it.

So, I followed the instructions to move it to my iPod by using Apple Device. I can see the music on my iPod inside of Apple Device but not in Apple Music to transfer over. I've used the search feature and also gone thru the list and I'm 99 percent sure I'm seeing music on my iPod ... what do I need to do in Apple Device to see music in Apple Music. I feel I'm so close. Here's a screen shot from Apple Device:

I don't have automatic sync turned on. I just want to move this one new song. Thx