Muscle soreness is in large part individual thing and you need to experiment a bit to find out what works for you.
First thing I’d recommend is splitting your weekly volume in 2 workouts instead of once a week. Don’t add extra volume because that would increase fatigue, but just keep high load and intensity but split sets in 2 workouts. Muscle soreness is often strongest when doing new exercises and for some people training certain muscles once a week basically resets that novelty effect each time.
So I’d recommend couple of minutes of brisk walk or light jog on a treadmill just to warm your body, then some lunges just to get into movement and then couple of sets of heavier squats. Try that 2 times a week instead of once and you might see a big difference. I would also incorporate deadlifts, you can try adding them on same days or some other days, depending on your fatigue and soreness. You don’t have to go hard on them, you can do even do some variations at home with a kettlebell or dumbells.