I want the audio of one app to continue to play while using a different app

YouTube Premium version has this feature.

If you are experiencing any difficulty with third-party apps or a specific website then please contact the app developer or site publisher/host directly. Here is how

• To contact an App developer --> How to contact an app developer - Apple Support
• To contact a web publisher —> Scroll Down to the bottom of the web page. You will find: Contact Us, Help Center, Support, Terms of use etc.

The app playing the audio must be designed to work that way. Just about all streaming apps will.