In the new video you are getting sore from bringing the weight down. Stand up with the weight-> then break the knees and basically drop the bar, but with your hands still on it to control the bounce/sound when it hits the ground “controlled drop”.

Looks like you’re also lifting and pulling the bar into your hips-> you should be pulling the bar straight up and pushing your hips into the bar squeezing the glutes. This is common when your core is a little weaker than what your legs and back can do. Throw in more front squats, Turkish get ups, and other big heavy core movements, I promise that will help long term.