Do I need to pay for Apple Music subscription?

No. Apple Music is the streaming service. If you simply listen to songs in your library, or those you purchase through iTunes or the Music app, you do not need to purchase Apple Music.

Downloaded music that was purchased. Apple Music is not necessary. I don’t have a Apple Music subscription and my downloaded, purchased music works just fine.

Yes. The downloaded stuff is useless without it.

OP is enquiring about downloaded music, it won’t work without a subscription.