For whatever reason when I did that earlier, it was not grouping songs as albums OR listing the artists. I had a hot mess with all the songs listed individually and not being able to sort by album or artists is definitely not ideal. My Music app looked something like this:
Those are all songs from the same album, which ideally should just show the album name, not every individual song. The other thing is if you looked under albums, each song was listed individually, all with the same album name. If you looked under artist, the artist name was NOT shown on the list. I found a workaround, and while not ideal or pretty, it seems to work every time. Instead of dragging and dropping the complete album, I copied over one song, then a second one, and that grouped them together. At that point, you could copy over the rest of the songs and they were listed under one album. It seems to be a hit-or-miss if you copy over the complete album so I have just gotten in the habit of copying over a pair of songs first.
As shown on the last picture, that was the expected behavior. All the songs are now under one album and the artist is also listed under the library. Hopefully not too many people are experiencing this issue, but just in case, I hope it can help someone out.