this is actually a really cool set of ideas. this would be nice to try to replicate in my next baba is you level.
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if you really wanted to scare the player with a perceived difficultly spike of having many players, I don't think you succeeded. the level was not chaotic and if a level is simple, it is impossible to make it look difficult without introducing some new thing the player was not previously aware of. You need to have a level soon before this one which demonstrates how your level can be difficult (which as I said, is something ice puzzles naturally struggle with) and then still have at least one or two subsections of the multiplayer level which either replicate that difficulty or appear visually similar to it. alternatively, you could have one of the sections have an obvious linear solution and the rest be in some sense "auto levels" with work with the same solution.
I would recommend Relica Park, it is one of the best demonstrations of how to create a high quality story paired with high quality puzzle gameplay. even doing like 1% of the things it accomplishes in terms of vib would be very beneficial to any persons game I think.
if you want to learn about ways you can mess with a player's mind, I recommend playing some of theconspiracy's works, my personal favorite is "Side Effect." there's also "... in the blue" which explores some of the limits of what's possible with puzzlescript triggers.
as a puzzle game, I feel this would be better without the full text explaining every mechanic in the game, although I do like the way you did so unconventionally. I think you could probably keep that in if you have all of it be closer to the vibe of "Also, try to avoid from gray spot with a black center. Once you lose, you can restart level with "R" letter."
In terms of being an ice puzzle variant, I would like you to know that ice puzzles are one of the hardest types of puzzles to make interesting and not trivial. I think your mechanics definitely helped alleviate some of what makes ice puzzles so trivial, that being the lack of movement options that aren't just going back where you came from. And an interesting take to, adding a lock and key system to encourage backtracking. I would suggest adding some keys that are impossible to come back from though, requiring players to read the level and interpret its logic more. The needing to manage multiple players also has the potential to be interesting, it wouldn't be too difficult to attempt making a multiplayer synchronization maze, where there are many holes and only a few paths without holes, but I feel like that's not what you were going for here. nonetheless, I feel some people would appreciate the difficulty, as long as it doesn't gatekeep later levels of the game.
If you ever decide to add a new mechanic, I would suggest a reusable toggle button. Even if for a different game, I find that they can lead to a massive amount of deductive logic for a comparatively small level of effort.
in positions like this, X should almost never take the top-right space on their next turn (unless O takes center of course), as if they do, O can force them to take center and almost always have a guaranteed win (the exception being when there is another grid near the top-left of this and near the bottom-right, which is usually avoidable).

I like this. I actually made a trio of baba is you levels with a similar idea.
here are the level codes if you're interested (and have the game):
first: 9FEK-7GGV
second: BPJA-XUPZ
third: N8RY-JTB2
The first one is a good tutorial for the basics, the second one I'm not proud of, but lets you experiment with and understand some other key details, and the third one is the most difficult (remember to take into account what it says in the bottom middle for that one).
it just feels weird that there is just one tutorial level I guess. I wonder if it would be better if the tutorial and the main level were on the same screen? I don't really know what say in these situations, I agree there should be a tutorial somewhere in there to address potential ambiguity of what the win condition is, but at the same time, most things are either a standalone level or part of a set of levels.
perhaps you could just add one line of lore before and after, to increase the sense of compleation.


unbounded points possible for O start. I thought you said this AI got harder 
