A good way for me to break out of a squat stall is to basically hold the bar just like a normal squat start position and then breathe in strongly and out strongly 10 times then go down and up then 10 times again. This helped me break a 2 month stall I had on squat when I first started. After that, every last set of squat I do now is always the 10 breathe thing no matter how many reps I'm doing even if its just one. You're all probably going to think I'm crazy lol
I'm not sure if that really breaks any stalls. Lets think about it this way. You do squats for 10 reps. You take deep breath for 3-4 reps a time, or once every rep. There is not much break between reps. Then there's your methdod, where you breathe in heavily ten times between each and every rep. Think about how much break and rest you get between every rep. Practically what you are doing is 10x1 with 10-15sec rests, not 1x10 sets. There is a huge difference. There is a method called cluster sets, and you style is more resembling that. In the method you do lets say 4-5 reps with your 5RM weight, rack the bar for 10 to 15 seconds, then crank up another rep, maybe rest again, and then do more. That leads to total of 6-7 reps with your 5RM. But I could hardly call it one set of 7 with huge progress behind it.
The breathing is just giving you time to rest, what makes you get more reps and not fatique you out so quickly. I can't see anything else that it could benefit.