Is it not possible because the iPhone 8 cannot actually run 15.8.1, or because Apple wants to force an upgrade to iOS 16 and is therefore deliberately not singing 15.8.1 for the iPhone 8?
I suspect the answer is the latter because my iPhone 6s Plus has the update for iOS 15.8.1 ready for me to install. And if the 6s Plus can run 15.8.1…