I have Apple Music. But I’m still getting charged for every song I download.

Buying songs (one time payment) in the the iTunes Store is separate from the Apple Music subscription (recurring payments, while the subscription lasts).

To use Apple Music without getting charged for each song, do not get the additional content from the iTunes Store.

Make sure to log in with the same Apple ID as the subscription is for.

Search within Apple Music for content. The content should not list prices, as the content is included in the subscription, unlike the iTunes Store!

Add content from the search to your iCloud Music Library. Optionally download selected tracks for offline use from within your library, using the icon.