Can the App Store be installed on Xcode's iOS Simulator on the new ARM/M1 powered Macs? Years ago on Stack Overflow people already asked about installing the App Store on the iOS Simulator but the answer was you couldn't because the Simulator doesn't run ARM code but Intel code.

The Simulator does not run ARM code, ONLY x86 code. Unless you have
the raw source code from Apple, you won't see the App Store on the
Simulator.

So you can only run apps you're working on and compiling yourself, and the few that are preinstalled on the Simulator.
But as of very recently Macs now also run on ARM. So can the iOS Simulator on an M1 powered Mac have the App Store installed on it now?
No.  The iOS Simulator does not have an App Store.
There are many iOS Apps available in the macOS App Store on Apple Silicon Macs.