iOS - App Store Stories
There is no official way to access the data. However, there are some websites that offer similar functionality.

One website I found is Sensor Tower. It lets you see 3 day history for free, and up to a year if you pay. The feed appears as it would on an iOS device.

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.