Cross it back, suspension-supported, glutes lit up.
Use the straps for balance only. Keep your hips square to the front as you cross behind.
Crossing one leg back and behind the other puts the front quad in charge of a deep, slightly rotated squat pattern while the front-side glute gets loaded at an angle a straight-back lunge never finds. The straps are there purely for balance, letting you sink to parallel without hopping or tipping as the legs cross. It earns a spot for anyone building lateral hip strength and control, hitting the legs from a diagonal that standard lunges leave untouched.
The crossing step loads the hip at a diagonal, so the glute of the front leg works to control rotation and side-to-side stability as well as drive you up. Straight lunges never challenge that plane.
Some awkwardness while learning is normal, pain is not. Keep the cross shorter, keep your hips facing forward, and only deepen the position as it starts to feel smooth.
Either works, the steps allow both. Holding them at your chest gives a bit more balance challenge, holding the handles gives more support while you learn the pattern.
