To be clear, music that you have purchased, either from the iTunes Store, from other online retailers (such as Amazon or Bandcamp) and music that you copied into your iTunes Library from CD is neither "Apple Music" nor "iTunes".
It's music.
If you have music on your computer, that you have purchased, you should use the Android method of adding that music to an Android phone. The music can be listed in iTunes or not listed in iTunes. As long as it's on your computer (in a format that your phone can play), you can add it to an Android phone. The steps required might be mentioned in your phone's instructions, or online search should help you. It is not an iTunes function and iTunes cannot add music to an Android device.
None of this has anything to do with Apple Music or any subscription service.