Side lunge with the straps keeping you stable and deep.
Push your hips back over the bending leg and keep that knee tracking over your toes.
Stepping wide and sinking your hips back over one leg loads that quad through deep knee bend while the trailing leg stays long, and the glutes control the hip as you drop into a range most people rarely visit. The straps make the depth honest, offering balance so you can sit back properly instead of tipping forward onto your toes. It earns its place because training happens almost entirely front to back, and this loads the legs side to side where sport and life actually happen.
Squats load you straight up and down. The lateral lunge loads one leg while you move sideways, building the hip control and deep single-side strength that vertical work never touches.
Yes, along the inside of the straight leg is normal as you sink over the bent one. It fades as your hips adapt, keep the straight leg's foot flat and toes forward.
Your hips are not going back far enough. Push your hips back over the bending leg as you descend, and let the straps balance you so your chest can stay tall.
