https://nitter.net/SpaceX/status/1726316194649846026#m
Watch the three center engines on Starship’s upper stage gimbaling just after separation. Right before they ignite for hot-staging, the engines angle themselves outward to direct their exhaust towards the vented interstage before re-centering for ascent.
It’s not the same video indeed, so I was wrong. Plus your video comes from SpaceX itself, so that should be legit.
In my mind the booster flipped around much faster after staging (though the live stream wasn’t really detailed enough to show that).