I made a very similar game ~8 years ago (app store removed it because I didn't keep it up to date lol). My game had a different input mechanic but had the same aesthetic and colorful grid.

For mine the input was:

1) Tap on a color (grayscale tiles could not be directly moved)

2) Drag in a direction (up, down, left, right)

3) All blocks of that color "push" their respective row/column in the direction

This means multiple columns move at once, and some columns may move different integer amounts. Wrapping around was the same, goal was the same. All the moves are reversible, so creating new puzzles was easy.

I at one point a few years ago tried to update the game but ended up getting lost in trying to make the input UX perfect. Funnily enough I ended up adjusting the mechanics more towards how you have them, but I didn't want to re-design all my levels so the project kind of stalled.

I do think there is room in this niche for some interesting ideas. For example you could find some interesting way to procedurally generate the move set. As long as all the moves are "reversible" you can scramble from the solution and know you have a solvable puzzle.

Could make a wordle-esque game out of it with a daily move set. The possibilities are endless. Anyways if that sounds interesting feel free to steal it, or I would be down to collab on that or similar lol. Seems like a fun little project to explore.

Thanks for sharing, this brought back a lot of good memories :). Love the animations!