keeping windows in the external display after sleep/undock


I'm starting to play with the app and trying to understand if it can do what I need.

I'm transitioning from working with a Linux desktop to a Macbook Pro M3 with Sonoma 14.4.1. I have the laptop and an external display and the problem happens when I turn off "Displays have separates Spaces". Once I do that every time the laptop goes to sleep, or I disconnect the expernal display, or I just turn it off, all the windows in that display move to the main display and never go back to the external display once the computer wakes up.

The behaviour when the "Displays have separates Spaces" is that the windows go back to the external Display when the computer wakes up or the display is turned on/re-connected, which makes a lot more sense.

There seems to be an app called "Stay" that helps with this problem, but in the reviews someone talked about BTT being able to do this and much more. Can anyone tell me if this is true and how to do it?