We usually consider here that mouse movement uses at least 2 buttons already (x-axis, y-axis), so it's beyond the scope of this jam indeed.
But, well, if you have an original idea, you can go for it. It's better to make a game than nothing.
Or can can take part to the sister jam : https://itch.io/jam/2-buttons-jam-2022
In any case, good luck and have fun :)