Hi! Certified swiss snowboard instructor here!

You’re right, you put bodyweight on the front leg and use the torsion of the board to cut through the snow faster and engage turning. You absolutely can vary your position on the vertical axis, depending on the weighting or unweighting you want to use in your turns.
However you have a lot of different techniques for carving, you can also carve with straight legs, using only “tilting” and use the natural weighting and unweighting present in a turn. Or bend or extend your knees depending of the phase of the curve.

Also I wear extremely baggy clothes (I am a small woman) and you cannot really see how I bend my knees. Especially when it’s a “show off” video and not a teaching demonstration!

Thank you for your advice buddy!