This weeks TidBITS discussions mentioned people wanting app windows to always be located at specific screen locations whenever the app opens. There appear to be several apps that will allow that. However, those apps seem to be mainly for locating a particular (main) window for any app. But one reader mentioned using Keyboard Maestro (a macro creating app) to do this locating. I think you might have a solution awaiting your problem. I use a different macro app and don't know if it has this capability, but
Keyboard Maestro has always been a highly recommended and quite powerful app. It's not free but it does have a free trial.
Another solution may be a function already installed in the mac OS:
Spaces. I've never even used it and don't even know if it's still in Catalina, much less Big Sur. I think it is part of the Mission Control part of the OS, yet another set of functions I don't use.
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