Very cool, creative concept and fun to play -- awesome work! The artwork is great and background prompts are effective. The wrinkles you added along the way were also great and worked well. Like another commenter, I found myself yearning for a keyboard button rather than a mouse-click, but it did work!
I completed all 15 of the main levels. I died an average of 6.8 times per level on the first 14 levels, and then died 168 times on level 15. There is something that felt amiss on that jump in the lower right, right after getting the key and bouncing back to the left, that made me feel like double-jumping was disabled. I even wondered if double-jumping doesn't work when you fall from a platform rather than jumping from it, but no. I suspect it might be that the collider for the island spikes down there is a bit too large, such that the player clips it even when not hitting the spikes and the death animation begins when it feels like one should be able to click another jump. Just a guess. I hope that's helpful feedback.
Great work!