I wouldn't call it sluggish. It's just that the tiles only update on mouseup events, rather than on mousedown events. Your own finger's turtle speed is the only source of latency ;)

But I agree that applying different styling to tiles on both hover events and mousedown events would make it feel snappier.

(I've only tried this on desktop. Haven't tried it on mobile)

Yeah I get 100-250ms of latency between input and presentation. https://trace.cafe/t/UFXm7ASLQg

I get no interaction latency, perhaps because I made the tile size a little larger and there are fewer tiles. Give it a try. As someone suggested, the pieces only rotate which make it easier for finishing the puzzle.

What browser, OS?

On windows both Firefox and Chrome have no discernible latency for me at least.