WinUI 3 does not support kiosk mode, and it is only available for UWP, hence why it isn't showing up when you try to set it up for kiosk mode.

From the maintainer of the Windows App SDK which includes WinUI 3:

I discussed this at some length with the team that owns this area. The short answer is that at least for now kiosk mode is limited to UWP applications, and a change to that will require changes to the OS itself since there are some security model considerations.

Please consider opening this ask in feedback hub so it's tracked as a platform request. While the team is now aware of the gap, direct customer input is always appreciated.

https://github.com/microsoft/WindowsAppSDK/discussions/2653#discussioncomment-3450696

I wasn't able to find any workaround for this but as the maintainer mentioned, it would require OS changes which I doubt that you can bypass using just your app.

You can track #3642 on the microsoft/WindowsAppSDK repository for progress on kiosk mode. The thread doesn't have any workarounds I could find either.