As I wrote before, by default when you setup assigned access the UI only shows app which have the aboveLockScreen extension registered. I talked to the PM who owns this feature to ask why and the reason is because we changed the behavior of how assigned access works (lock the screen and launch the app above the lock screen) we found out a lot of existing apps crash when running on the lock screen, so we changed the UI to only show apps which are designed to run above the lock screen.
Although the UI might not show your existing apps anymore you used to run as kiosk app, you can still use those. Obviously you need to test if they work when running above the lock screen.
Besides using MDM or a provisioning package to configure assigned access you can also use PowerShell to setup your app to run. You can find the documentation over here.
You will also find interesting documentation how to setup auto login and how to make a classic windows app the default app on that page as well.
This experience is something MS wants to improve in the future but for now you have to use this trick to setup your old app as assigned access app.