Love the background, UI polish, and the trail when cutting!
At first I thought it was just Hashi but with diagonal lines and was really confused on the second level. It took a bit of time to read and re-read the instructions before I saw the stars with a black outline meant size of connected component. The puzzle mechanics are great once I got that, I think it would have helped to invert the colors on the second type of star to distinguish them more.
The puzzles themselves were also great, I think a few of the ones I played had non-unique solutions. It looks like the puzzles are randomly generated after the first couple intro levels right?