Which version of iOS is required for the app? Usually, that information can be found by looking at the app details in the store, scrolling down to the paragraph headed Information and looking for the heading Compatibility. Until you expand the Compatibility section, you may not see the text about the specific iOS version.
I don't have a 7th gen iPod Touch but I believe that iOS 15.8.4 is now available (from 29th March 2025). Perhaps the app simply requires that version of iOS. However, if the app requires a higher version of iOS (for example iOS 16) then your iPod will not be able to use that version of the app.