Interesting, I was hoping the first three levels would establish the walls well enough, but I do suppose it would've been clearer if there was an early level that had more of them, presumably in a narrow corridor where the player could be forced to move around them. If you have a rough description of which level the difficulty jump took place in it may be helpful.
Also, there is indeed a slight cooldown on movement unless all movement keys are released. Said cooldown is slightly longer (still only around 1/3 of a second) following the first move after a key press. This is to reduce the amount of missteps that occur. The one that felt laggy is probably the one for the initial step, but without it, it is somewhat easy to accidentally move two tiles instead of one.