Moving an app from 6th gen iPod Touch to iPhone 15

had an app i purchased on my ipod 6th gen it still works minus the network features, i won't to put it on my new appel device but when i go through app history it won't show up and it no longer in app store. I try using the iTunes app and that no longer shows an app option that lets you select and individually back up all your apps, and re download it when you want to.

[Re-Titled by Moderator]