Pretty much this. Plenty of guys have used both methods. Classic thinking is to do it first in the routine when you've got the most energy and can go 100% balls out on it, like you'd do with any exercise/bodypart you wanted to prioritize. Overall programming is still going to be key though. You wouldn't want to do the squats and then knock out another 25 sets for two or three other bodyparts.
The flip side approach is to do it as the last move of the day so you don't have to "hold back" anything during your session hoping to preserve energy to get through it. Doing the squats last also means you don't have to "hold back" during the squats in anticipation of having another half hour of training afterwards.
Doggcrapp training has their "widowmaker" high-rep leg set as the last exercise of the day. The classic Super Squats program actually has the squats in the middle of the workout, after some low-ish volume upper body work. In the 1930s, 20-rep squats were superset with pullovers but done after overhead presses and curls.
Also, I definitely suggest taking 2-3 breaths between each rep from the beginning instead of starting the deep breathing at rep 10. It allows a slightly heavier weight overall, a little better focus on form (since you're "only" doing singles the whole time), and is how it was done back in the day.