"Purchase" or download GarageBand on that newer device to link it to your account history. Return to your iOS 15.7 device, go to
https://cloud-archive.net/files/garageband_1.5.7_legacy.ipa garageband ios 157 download link
If you want step-by-step instructions for installing a specific older version (1.5.7) from an existing purchase or device backup, tell me whether: "Purchase" or download GarageBand on that newer device
(Invoking related search suggestions.)