Both options are viable! Either she can inherit some powers from the belt, or the belt itself can be the source.
If the belt is the source of her powers, you could have it so it was damaged as she was brought through to the Legion's universe. The Time Trapper, the cosmic being that brings the characters to the game universe, is very powerful and tends to alter people's powers in ways he thinks make them fit well in a team. So she could have the belt and it'd just be damaged and not at full capacity during her time in the game.
So it's your choice what the source of the power is, and our main requirement is just that whatever power(s) are kept fit the 1, 2, 3 rule.
no subject
If the belt is the source of her powers, you could have it so it was damaged as she was brought through to the Legion's universe. The Time Trapper, the cosmic being that brings the characters to the game universe, is very powerful and tends to alter people's powers in ways he thinks make them fit well in a team. So she could have the belt and it'd just be damaged and not at full capacity during her time in the game.
So it's your choice what the source of the power is, and our main requirement is just that whatever power(s) are kept fit the 1, 2, 3 rule.
Does all that help?