Great video, thanks for posting. They show a few things really well:
1. Minimal body movement during the jibe.
2. The mast stays perpendicular over the board for the flip. Since the board is tilted into the turn, the mast also leans into the turn.
3. No rush in moving the feet after the sail flip. In waves or chop, sail a bit further until you have a smooth stretch of water.
I have verified multiple times on the water that deviating from any of these rules is an excellent way to induce crashes

. On the slapper, you can move a lot, but on the foil, any body movement causes direction changes and/or instability. On the slapper, you move the mast to the outside, especially with big slalom sails; on the foil, that stops the carve. When carve jibing on the slapper, I usually want to switch feet quickly after the sail flip; on the foil, I may not have carved far enough, or may be going up or down a big piece of chop.
Regarding carve jibe versus step jibe on the foil, the decision depends a lot on your speed relative to wind speed. On freeride foils, we're usually a bit slower than the wind, so the carve jibe (more descriptively called "sail first jibe") works well. On race foils, the speed is often significantly above the wind speed. Since you loose very little speed carving downwind on the foil, that means you have apparent wind coming at you when downwind - you can't flip the sail by opening up and letting go with the back hand. If you try to push it around, you get backwinded. So you slice the sail forward, and then do a helicopter-tack like sail flip, as Nico shows in his video. That's why the racers all step jibe on the foil.
The step jibe is also doable when foiling slower than the wind on freeride gear. But you move your feet at the same time as the sail, and with the higher sensitivity of the foil compared to the slapper, small mistakes can throw you off quickly. The higher speeds on race foils stabilize things a bit here, and the wider boards probably also help. But the carve jibe on (slower) foil gear is easier, since you can concentrate on one thing at the time. The movie demonstrates that very nicely, especially the first jibe.