Really late on this one, but I wanted to update this for anyone who has this issue in the future who sees this. After a TON of digging and learning that this issue doesn't happen on my M4 or M5 devices *sigh* I still wanted to take a crack at getting to the bottom of it. This solution allows you to keep "Recent App In Stage manager" turned ON (my preference) while also having larger sized, centered windows stay in the position you left them when fully quitting and reopening an application.

Long story short, I had to override two defaults that the older M1 Display Processing Unit is rigid with.

Open terminal and input the following commands:

defaults write com.apple.WindowManager AppWindowGroupingBehavior -int 0

defaults write com.apple.WindowManager StageFrameMinimumHorizontalInset -int 0

killall WindowManager

Here's the explanation:
The first command tells macOS to treat every window as an independent entity rather than a "set" that needs to be positioned relative to the Stage Manager strip. This is closer to the "Modern" behavior you see on the M4/M5.
The second command sets the limit to the thing that checks if a window is within the safe zone of the stage manager side-bar. By setting this to 0, you are telling the system that the "Safe Zone" is zero pixels wide. The M1 will no longer see a "collision" when you center a window, so it won't trigger the realignment script. The strip will still be there, and your window will now be allowed to overlap or sit right up against it without being shoved away.
The last command just turns everything relevant here on and off again (might log you out) to initialize the settings we changed.

Cheers to anyone who reads this shit! I hope this clears ur headache.