How do I listen to the music I paid for without a monthly fee?

Purchased music is available in the Music app or in the iTunes app on older macOS and on Microsoft Windows, whether the music was purchased from Apple or another provider, or downloaded from a provider offering openly-licensed music, or music acquired from a CD you've imported.

Rented music acquired from (for instance) Apple Music service is only available for as long as you've rented it.

If there's rented music you're interested in from Apple Music or another service and that you wish to keep, that'll require purchase.

Hello,

If you're talking about iTunes music it should still be in your Music App.