Purchased iPad app does not show up in list of purchased apps on my M1 MacBook Air

Just because the Mac’s chip can run iOS and iPadOS apps doesn’t mean the maker, ie developer, lists it that way. The maker of this app has decided to sell it by OS, so the iPad version will not be useable on the Mac. You’ll have to buy the Mac specific version they offer.

It's entirely possible the App is not set to be installed on a Mac by the developer. Even though apps can run on M1 Macs, they must be set by the developer to do so.

If its not in your Purchases history, its entirely possible it has not been set up to allow it to be downloaded on an M1 Mac.

It will just appear in the search results, but may not allow the download.

When I search for Art Authority, it says it has not been verified for Mac:

See if anything here helps.

https://www.macrumors.com/how-to/install-any-ios-app-m1-mac/#:~:text=Apple%27s%20M1%20Macs%2C%20which%20are%20the%20first%20to,to%20the%20MacRumors%20YouTube%20channel%20for%20more%20videos.

https://youtu.be/BNvHqrXoc9c

https://youtu.be/PHtPpU_RQi0

https://youtu.be/MlJ-zOCtck0

can m1 chip macs run IOS apps

It sounds like the Mac version of the app and the iPad version of the app are two different apps/applications that the Developer decided to sell separately.