I downloaded the program, but it only takes me to the free version from the start screen. When I try to add more than 8 tracks, for example, it tells me I need to upgrade to premium version.
I'm not sure what you mean by register. However in my 2021 version I go to the account tab in the start window pop up and there's a place to put the serial number and an activate button to press. I don't know what things look like in the the latest version.
See this that hopefully goes to my thread showing the steps to get the program, Music Maker 2022 up and running and Premium Edition activated.
Once in the program and logged in and updated and everything has been downloaded and installed, go to the Project Settings and you'll see the option to increase the number of tracks.