When does run up end?

I understand the letter of the law on feinting at a penalty kick. Permissable until the run up is complete. My question: is there a clearly defined moment that completes the run-up? Watched several PKs in the Europa and the Americas that seemed awfully close. Player runs up at one speed, plants and pulls the foot back at the same speed, and then pauses just enough for the keeper to move before kicking the ball. So is there clear guidance on the moment the run-up ends?

I would suggest that as soon as they plant their non-kicking leg the run up is over. The Laws however say nothing about pausing here, merely "feinting"; in other words pretending to kick and then not doing so.

The run up is finished when the player arrives at the ball and does not thereafter take any more steps before kicking the ball (or feinting to kick it, if they breach this part of the law).

If you saw players plant their foot, draw it back, then pause and wait until the keeper moved, before then kicking the ball (and without taking another step before kicking the ball) then those players broke the law.

I didn't watch the Copa America so I can't comment about those games but nobody did that in the Euros. I watched every game and in fact even watched replays of some of the penalties to make sure the law wasn't broken.

In all cases after feinting, the player took at least one more step before kicking the ball - and I'm sure about that because I made a point of checking all the ones that looked close in real time.

Perhaps the point alluded to in OP is varying the speed of 'forward momentum' after the run up is complete (generally considered when the non-kicking foot is planted next to the ball) and before the ball is kicked.

There are a few penalties I have seen that the taker is in an almost paused state as soon they land their non-kicking foot, usually preceded with a hop. The kicking foot going back mentioned in OP is a likely referring to the normal movement of kicking in a slow run up or no run up to kick the ball and not a feint to click the ball.

As the law is written now, varying the speed of movement even after the run up is complete is not an offence. For lack of a better description, reversing or pulling out of a kicking action after the run up is complete is an offence.

In other words the kicking foot going backwards after the non-kicking foot is planted next to the ball is not necessarily a feint or an offence. Try taking a kick with no run up or a very short last step. Kicking foot goes backwards almost everytime.