Purchased Songs not Matching with Apple Music

Hi to all!

SUMMARY: Some iTunes purchased songs don't match with Apple Music downloaded ones, so my iPod and weekly Apple Music charts are being problem.

For some time I'm in the nostalgia of using an iPod. Thus, I purchased some songs from iTunes Store, which I already had in my Apple Music library. So far, I hadn't had any problems. All the songs were merged, including their play counts. My weekly Apple Music charts were getting updated no matter where I listened those songs, on my iPod, MacBook, or iPhone.

However one day, my girlfriend deleted 4 albums of songs using my Apple Watch as a joke. After I added those songs to my library back on my MacBook, they didn't appear on my iPhone. Then I added them using Apple Music search to my library. Later I realised all of those songs were duplicated (only on my Mac). Listening counts were not matching, and only the ones added from my Mac were downloaded. When I downloaded the duplicates, they were being downloaded as Apple Music files, which are not compatible to sync with iPod.

This issue only appears for these songs, which were deleted on my Watch. None of the other songs I added through Apple Music and later purchase are duplicated. However these 4 albums are making me crazy. If I add them through Apple Music interface they are not compatible with my iPod. And if I add them through iTunes Store, they don't seem to be getting into the weekly Apple Music chart, which I actually like checking.

All the listening counts have been reset as well. I also know that currently the weekly charts are not available (due to new year) but this problem have been going on for more than a month. Is there a way to solve this problem?

Thanks in advance.