Pretty cool idea!
I enjoy that this was a grid based version of the "avoid your past self" mechanic. Since it allows for much more intended solutions and thought out moves.
At first I thought it was going to be a set of puzzles that were just 2 rooms, where you would need to do it twice though. But learning that the levels went even more rooms (5) deep was really cool. Having to go back to the start to rethink everything.
I think this game could benefit from some more clarifying visuals, I think the best puzzle games are the ones you can look at without doing anything and think about what you'll do. But its hard to do so on this game, since you can't see what the later rooms will look like. I found that it essentially boiled down to moving the most you can each level, then each next level just move 1 less, which the moves remaining helped to keep track of.
Having more groups of rooms would also be nice, since it would then also give the player the feeling of accomplishment for beating a puzzle. But I get that it was a short jam so time was limited.
Lots of room here for more mechanics and additions.
Maybe I'm wrong, but it sometimes felt like my past self wasn't actually repeating all the steps I took in the last level.
Nicely done!