I am also seeing this bug, but we additional information. I had 2 iMacs (21,5", 2017). The first one was updated yesterday using a clean install with a bootable usb-stick. Everything works perfectly, including the App Store. The second one was updated today with the same USB stick and the same method. In this case, I started to see the bug ("No purchase" in App Store). I tried log out/log in, reformat 4x, etc. etc. etc.
Thus, I guess the problem is seeing by people who installed macOS Catalina today.
UPDATE: The problem is so strange that even if you download an app, it will not shown on the list in App Store. If you delete, it will ask you to buy it again.