Kind of confusing at first; agree that a more organized/intuitive UI is needed. When transitioning from opening to first puzzles, maybe include some pop-up text boxes explaining the sides tracker and goals section?
UI suggestions: might not need to have "goals" as the header on the right section- just include a list of goals. Might also be able to do without the "total sides"- just have a number that increases/decreases.
Since this was made for a jam (perhaps under time constraints), I don't want to be too picky, but it would be better to avoid lettering the colors (e.g. "color B shape"); having to remember which letters correspond to which colors adds mental overhead and distracts from the actual puzzle-solving.
Otherwise I think it's a nice concept!