Those are great exercises! No way I am putting a knee to the ground though. I did manage to get off the floor on hands and feet yesterday, same way I used to. It has been a whole year and I lost confidence in being able to do it. I used to do backwards lunges as forward was too much for my sore knees. Also my PT tells me to have feet apart, knees over toes when doing things like this. I could sit to stand off my recliner! TKR wasn't happy about it, pulled a lot more than the natural knee but did it fine.
Start by sitting down slowly. I used to catch the seat with my hands to be sure I was going to land safely. Getting control of going down is hard work. I still use my hands to get off my recliner and am thinking maybe if I try using only fingers, then only half the fingers might be transitional enough for me. Practice sitting and standing at many levels as well. My highest was the commode, next the bed, the dining chairs, the window seat, the sofa and lowest is my recliner. I could bounce off the bed which is definitely cheating but if it builds confidence in your muscle strength then it is a good idea anyway! And I don't do squats as an exercise, it is super hard on my knee.I get up lots more than I need to but no sets with reps for me.