The ONLY way I have found to play externally downloaded mp3 content is to download a third party app that is capable of importing ( sharing ) these mp3 audio files and playing them.
In the dowloads folder in the Files app, you will need to use the share icon/feature ( square icon with an upward facing arrow ) to import/share these files with another audio playing capable third party app.
Apps that I have found that work are third party paid notes apps with audio recording/playback capabilities/features.
The ones I have/use are
GoodNotes
Notability
Zoom Notes
Once you have paid/installed one of these apps to your iPad, In the downloads folder, in the Files app, you tap the square Share icon feature and look for one of these apps in either the horizontal or vertical app selection menu to share/copy/import these mp3 files into one of these apps and play these mp3 audio files within one of these third party notes app.
This has been THE ONLY way I could find to play externally downloaded audio files outside of the Apple Music app.
Best of Luck to You!