See history of Today tab iOS App Store
Related: iOS - App Store Stories

The maximum you can look back for is 7 days. There is a website called Sensor Tower which lets you see up to 365 days but it requires a subscription. 

Alternatively, for some stories, you can tap on the Share Story button shown at bottom, copy the link and send it to yourself. However, this approach is highly manual, would have required following it since the day App Store redesign was publicly launched. Also, it is not possible to do so if you want to start out today as the older feed entries can no longer be accessed