https://github.com/koekeishiya/yabai
I used to use BetterTouchTool and Stay to do this, but after a co-worker tipped me off on yabai+skhd, I've been extremely pleased and rarely have to think about window placement (took me a while to get the config "just right", of course).
I haven't tried it on Big Sur, but because of the way yabai can assign windows to spaces, I don't believe you'd face this issue.