The puzzles are fun to figure out! The core mechanics of the game are great and I'm sure you could make many levels out of those. I think it has just the right amount of mind-bending while still not having too much to think about ("there are only so many possible moves I could do, this can't be that difficult"). The levels not being too busy is a good thing. There were definitely a few "aha" moments in there.
The controls are a bit hard to grasp and while I do see the effort you made to make them clearer I think the game still needs a bit more, notably with the vertical shift mechanic. I think all the controls being always on-screen with a visual indication of what they will do would be the best. Thankfully, the undo being always available makes this a relatively minor issue.
While I was stuck on one of the levels, I encountered what I think is a bug or half-implemented mechanic allowing me to walk on a box when it's on the side of a white block. At first I thought this was the solution, but as soon as I started shifting it started to break, with the box and the cat moving to impossible floating positions. (The actual solution involved falling through the edges of the screen which was quite clever). I'm sure you could make levels out of that mechanic though, once you fix it!
As a minor nitpick, I think the vertical shift takes just a bit too long and the sound is just a bit too annoying for an action you're sometimes meant to do several times in quick succession.