According to the App Store description – and the MLB Support page to which the App Store page links – the current version of the MLB app requires iOS 16.0 or later.
https://www.mlb.com/apps/mlb-app/faq-apple
"Supported Apple devices must be running a 16.0 or greater operating system."
"If you have any questions or require troubleshooting assistance, please visit mlb.com/support."
If you have an old version of the app, It might run on iOS 15, but there's no guarantee that it would continue to work properly with the MLB service.
You can update an iPhone 7 to the latest release of iOS 15 – but cannot update it to iOS 16 or later.