This really subverted my expectations of a sokoban game.
It reminded me of mechanics from a game called "loopholes" . But I've also seen similar time puzzles in Talos + a portal mod called thinking with time machines. However I think you actually use them in a more creative way because it switches the "solving" players focus between the first/second/third character.
I really think that Level 4 needs better tutorialisation. I solved it the first time without realising that my inputs were being recorded and then played back. So I didn't understand that was useful or needed for Level 5. Although once it clicked I enjoyed completing every puzzle.
I can see it being a pain to properly demonstrate this mechanic in an elegent way - but it needs a clearer example. Also reseting might be more useful on several buttons.
Overall this had really creative puzzles, and I think there's more to explore there.