Unfortunately Stage Center is a mess. It is correctly centered here because the area Stage Manager reserves actually goes almost to your red line. (Stage Manager always reserves about 10% of the screen width)
However if you'd like to change space BTT leaves for Stage Manager, you can adjust it here:
I have the settings set to leave a 10% gap, and when I drag, I can see a white line that represents the gap, but neither the preview nor the final window position have a gap — they both go completely to the left side of the screen.
Attaching a screenshot of settings and video using snap area.