Caught In An Infinite Update Loop

I'm trying to continue running the MLB app on this device, but a few days ago I started getting a message telling me I needed to update to a newer version. When taken to the App store, the only version of the app that's displayed indicates that iOS 16 is required, but of course iPod Touch can't upgrade beyond iOS 15. There is an "Open" button, but when tapped I go back to the iPod where the original app restarts. The "Update required" message comes back up, so I'm forced to go round and round between App Store and iPod. The only way to get out of the loop is to close the app. What is really strange is that I have a first generation iPhone SE that is also running iOS 15.8.2, and the MLB app works just fine, no prompt to update. I've tried everything I can think of to try resolving the problem, including power cycle, restoring from earlier iCloud backup where the app worked OK, even resetting to factory defaults. After doing the complete restore, I've discovered that a couple of my other apps may not work either because of getting into the update loop because the current version of that particular app is no longer supported. Has anyone else run into this problem, and if so have you found a workaround? Many thanks!