I don’t see any point in using variables to change the radio instances, unless you want one button collection affect the other one, e.g. you only want the user to be able to select either email or mobile app; not both, but that doesn’t make sense in this case. You also lose the ability to animate the component when using variables to change variants.
You can simply add or subtract from an integer variable that tracks how many buttons are checked. Then use a string variable for the state of the continue button.
It is very similar to this solution (you can open it and inspect the design):